ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • American Institute of Physics (AIP)  (9,575)
  • 2010-2014
  • 1995-1999  (9,575)
  • 1998  (9,575)
Collection
Years
  • 2010-2014
  • 1995-1999  (9,575)
Year
  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4417-4429 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Silverstone [Phys. Rev. Lett. 55, 2523–2526 (1985)] has expressed the opinion that the traditional version of the JWKB connection formulas associated with a classical turning point is incorrect and that the correct version follows from the Borel-based summability of the asymptotic expansions for the Airy functions. In the present paper we show that this assertion is incorrect. After the Borel summation of the asymptotic expressions for the Airy functions has actually been performed explicitly, there are no connection problems, and thus no connection formulas, but exact relations expressing the functions Ai(z) and Bi(z) in terms of the Whittaker function, although with two defects: Due to the derivation there appear false restrictions on arg z, and there is an artificial cut that coincides with the Stokes line along the real z-axis. We also show that these exact relations can be obtained more appropriately in a direct way with the aid of standard formulas available in handbooks, whereby the defects mentioned do not appear. On the other hand, when one uses truncated asymptotic series, the Stokes phenomenon gives rise to connection problems, and the connection formulas, which one uses for handling these connection problems, are inherently one-directional. This property of the connection formulas is demonstrated and discussed anew, in general terms as well as with special regard to the Airy functions. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4449-4475 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Chiral U(1) anomaly is derived with mathematical rigor for a Euclidean fermion coupled to a smooth external U(1) gauge field on an even dimensional torus as a continuum limit of lattice regularized fermion field theory with the Wilson term in the action. The present work rigorously proves for the first time that the Wilson term correctly reproduces the chiral anomaly. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4430-4448 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Low energy effective actions are computed by integrating out degrees of freedom heavier than some energy scale of physical interest. At the one-loop level, the low energy effective action can be computed in terms of the functional trace of the heat kernel associated with the operator appearing in the part of the action quadratic in the heavy fields. Here, a technique for computing this functional trace is illustrated in the case of heavy scalar fields coupled to a Yang-Mills background. It makes use of the similarity of the functional trace of the heat kernel expressed in momentum space to a Gaussian integral. An explicit computation of the piece of the low energy effective action for the Yang-Mills fields quadratic in derivatives of the field strength is carried out, extending previously known results on the form of the long wavelength limit of the low energy effective action. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4634-4663 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The semiconductor Boltzmann equation is considered within a material with a space-dependent band characteristic. Its fluid limit under strong elastic collisions leads to the so-called spherical harmonics expansion (SHE) model. For this model, the influence of smoothly space-dependent or abruptly discontinuous band characteristics is analyzed. For the latter case which occurs at heterojunction interfaces, kinetic boundary layers are analyzed and higher order transmission conditions are derived. In a further step, transmission conditions through heterojunctions for the energy-transport and drift-diffusion models (which are obtained as moments of the SHE model) are constructed. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4683-4700 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is proposed. It starts with the generalized Hirota identity for the Cauchy–Baker–Akhiezer (CBA) function and leads to a generalized KP hierarchy in the form of compact functional equations containing a special shift operator. A generalized KP hierarchy incorporates the basic KP hierarchy, modified KP hierarchy, KP singularity manifold equation hierarchy, and corresponding hierarchies of linear problems. Different "vertical" levels of the generalized KP hierarchy are connected via invariants of the Combescure symmetry group. The resolution of functional equations also gives rise to the τ function and the addition formulas for it. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4701-4728 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An analytic-bilinear approach for the construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered. This approach allows us to represent generalized hierarchies of integrable equations in a condensed form of finite functional equations. A generalized hierarchy incorporates basic hierarchy, modified hierarchy, singularity manifold equation hierarchy, and corresponding linear problems. Different levels of generalized hierarchy are connected via invariants of Combescure symmetry transformation. The resolution of functional equations also leads to the τ function and addition formulas to it. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4746-4758 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We use a factorized L operator to construct an integrable model with open boundary conditions. By taking the trigonometric (τ→−1∞) and scaling limits (w→0), we get a Hamiltonian of a classical integrable system. It shows that this integrable system is similar to those found by Calogero et al. [J. Math. Phys. 10, 2191 (1969); 12, 419 (1971)]. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4785-4813 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The discrete version of the inverse scattering method proposed by Ablowitz and Ladik is extended to solve multi-component systems. The extension enables one to solve the initial value problem, which proves directly the complete integrability of a semi-discrete version of the coupled modified Korteweg–de Vries (KdV) equations and their hierarchy. It also provides a procedure to obtain conservation laws and multi-soliton solutions of the hierarchy.© 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4891-4898 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Gowdy space–times are generalized to admit two commuting spatial local Killing vectors, and some new varieties of them are presented, which are all closely related to Thurston's geometries. Explicit spatial compactifications, as well as the boundary conditions for the metrics, are given in a systematic way. A short comment on an implication of their dynamics toward the initial singularity is made. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4948-4964 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider quasilinear parabolic equations with gradient diffusivity ut=div(|∇u|σ∇u)+f(u), x∈RN, t〉0, where σ≠−1 is a fixed constant and f(u) is a given smooth function. We also study quasilinear parabolic equations with a gradient-dependent coefficient ut=h(|∇u|)Δu+f(u), with a smooth function h(p). For both classes of equations we derive first-order sign-invariants, i.e., first-order operators preserving their signs on the evolution orbits {u(⋅,t),t〉0}. We give a complete description of (maximal) sign-invariants of prescribed structures. As a consequence, we construct new exact solutions of some quasilinear equations. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 11
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4928-4947 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Clifford geometric algebras of multivectors are treated in detail. These algebras are built over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear that opposite Clifford algebras have to be used for obtaining all endomorphisms. Based on these mathematics, we give a fully Clifford algebraic account on generating functionals, which is thereby geometric. The field operators are shown to be Clifford and opposite Clifford maps. This picture, relying on geometry, does not need positivity in principle. Furthermore, we propose a transition from operator dynamics to generating functionals, which is based on the algebraic techniques. As a calculational benefit, this transition is considerably short compared to standard ones. The transition is not injective (unique) and depends additionally on the choice of an ordering. We obtain a direct and constructive connection between orderings and the explicit form of the functional Hamiltonian. These orderings depend on the propagator of the theory and thus on the ground state. This is invisible in path integral formulations. The method is demonstrated within two examples, a nonlinear spinor field theory and spinor QED. Antisymmetrized and normal-ordered functional equations are derived in both cases. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 12
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5007-5014 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We construct the vector space dual to the space of right-invariant differential forms constructed from a first-order differential calculus on inhomogeneous quantum groups. We show that this vector space is equipped with a structure of a Hopf algebra which closes on a noncommutative Lie algebra satisfying a Jacobi identity. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 13
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4729-4745 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Drinfeld–Sokolov construction of integrable hierarchies, as well as its generalizations, may be extended to the case of loop superalgebras. A sufficient condition on the algebraic data for the resulting hierarchy to be invariant under supersymmetry transformation is given. The method used is a construction of the hierarchies in superspace, where supersymmetry is manifest. Several examples are discussed. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 14
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3600-3618 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For a quantum-mechanical particle without interaction, a linear manifold of states is identified that has a preferred time direction pointing to the future. States with the broken time-reversal symmetry are singled out by their behavior under dilations. At positive times such states can be described in terms of a density operator with the property that the trace of its square decreases as the time increases. This density operator determines an entropy that approaches its least upper bound when the time tends to infinity. The expectation value of the dilation operator was negative in the distant past and will be positive in the remote future. This is the irreversible aspect of the time evolution that causes the entropy to increase, although there is no approach to equilibrium. The density operator with increasing entropy is obtained from the usual density operator by an invertible transformation that is compared with the Λ-transformation in the Prigogine theory of irreversible behavior in K-systems and large Hamiltonian systems with many resonances. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 15
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3661-3669 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The duality transformation described by Arnol'd, which relates the orbits for different central potentials through a change of variables, is shown to be an example of a generalized canonical transformation, in an extended phase space that includes time as a dynamical variable. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 16
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3711-3729 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of (nonlinear) transformations to the solution of the linear differential equation. It is also shown that similar concepts apply to the nonlinear Schrödinger equation. The role of symmetry is discussed. Finally, the procedure which is followed in the one-dimensional cases is successfully applied to find special solutions of higher-dimensional nonlinear partial differential equations. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 17
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3619-3642 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Similar to the Beltrami parametrization of complex structures on a (compact) Riemann surface, we use in this paper the Kodaira-Spencer deformation theory of complex structures on a (compact) complex manifold of higher dimension. According to the Newlander-Nirenberg theorem, a smooth change of local complex coordinates is implemented with respect to an integrable complex structure parametrize by a Beltrami differential. The question of constructing a local field theory on a complex compact manifold is addressed and the action of smooth diffeomorphisms is studied in the BRS algebraic approach. The BRS cohomology for the diffeomorphisms gives generalized Gel'fand-Fuchs cocycles provided that the Kodaira-Spencer integrability condition is satisfied. The diffeomorphism anomaly is computed and turns out to be holomorphically split as in the bidimensional Lagrangian conformal models. Moreover, its algebraic structure is much more complicated than the one proposed in a recent paper [Losev et al. Nuc. Phys. B 484, 196 (1997)]. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 18
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3643-3660 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new and conceptually simple derivation is presented of the time-dependent multipole expansion of the electromagnetic field radiated by a time-varying, localized, volume charge-current distribution. The analysis is based on a new time-dependent plane wave representation of the electromagnetic field (i.e., an "angular spectrum expansion" in the time domain), also derived in the paper. Expressions are given for the time-dependent plane wave spectra in terms of a fourfold Radon transform representation of the transverse current distribution. Two alternative expressions for the time-dependent multipole moments are derived; the first gives them in terms of the spectral amplitude vectors of the corresponding time-dependent plane wave representation while the second gives them in terms of a weighted radial-temporal average of the current distribution. Thus the analysis also sheds light on the relationship between the time-dependent plane wave and multipole expansions in their common domains of validity. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 19
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3730-3737 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A supersymmetric extension for an arbitrary number of odd parameters of the stationary KdV equation is studied; we call this an N-extended super KdV. It is shown that it is related to superelliptic curves, and thereafter the complete ring of superdifferential operators commuting with the associated Schrödinger operator is constructed. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 20
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3754-3764 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For the equations describing second harmonic generation (SHG), we find a linear system different from one found by Kaup (but connected with it by a gauge transformation), which enables us to consider the SHG equations as related to the first negative flow in the coupled KdV hierarchy and to find therefore the Hamiltonian structures and the recursion operator. With the help of the recursion operator we write down the simplest commuting flows and consider their stationary points in order to find particular solutions of the SHG equations. We also investigate some particular invariant solutions of the SHG equations that can be of physical interest, and find their connections with invariant solutions of the Tzitzéica equation. The latter are either connected with Painlevé III or solvable in elliptic functions. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 21
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2499-2506 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Canonical quantization of the isomonodromy solutions of equations integrable via the Inverse Scattering Transform leads to generalized Knizhnik–Zamolodchikov equations. One can solve these equations by the off-shell Bethe ansatz method provided the Knizhnik–Zamolodchikov equations are related with the highest weight representations of the corresponding Lie algebras: These solutions can be written in terms of multi-variable generalizations of special functions of the hypergeometric type. In this work, we consider a realization of the above scheme for the Maxwell–Bloch system with pumping: quantum states for this system are found in terms of the multi-variable confluent hypergeometric function. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 22
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2564-2583 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We discuss a formulation of the level statistics for quantum systems that lie in an intermediate regime between the integrability subject to Poisson statistics and the full chaos subject to Gaussian statistics of the typical random matrix theory (RMT). It is based on the idea initiated by Yukawa and also by Nakamura and Lakshmanan, namely, to transcribe the eigenvalue statistics into statistical mechanics of the completely integrable Calogero system with internal degrees of rotation. By analyzing the previous works of Gaudin and Forrester from this viewpoint, we answer the question raised by Mehta and Dyson in early RMT concerning the expectation of compressible level gas, which is realized now in such an intermediate regime. It indicates the general absence of a fractional power dependence of the two-level correlation function under the ordinary thermodynamic-limit procedure as the manifestation that a transition between localized and delocalized states does not occur. The predictability of the transition by modifying the theory is remarked. Two applications of the present scheme are shown: the information loss per level and the correlation hole of survival probability for intermediate circular unitary ensembles. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 23
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2584-2591 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We propose a path integral formulation of noncommutative generalizations of space–time manifold in even dimensions, characterized by a length scale λP. The commutative case is obtaind in the limit λP=0. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 24
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2103-2111 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We give the conditions for a system of N-coupled Korteweg de Vries (KdV) type of equations to be integrable. We find the recursion operators of each subclass and give all examples for N=2. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 25
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2035-2076 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The one-variable Fokker–Planck equation is studied in a scattering formalism. Scattering processes are represented by paths in one-dimensional space, and the paths are treated as algebraic objects that constitute infinite-dimensional representations of SL(2, C). Various expressions for the scattering coefficients are derived in a systematic way by means of algebraic methods with considerations on symmetries. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 26
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 1534-1550 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A generic stochastic method is presented that rapidly evaluates numerical bulk flux solutions to the one-dimensional integrodifferential radiative transport equation, for coherent irradiance of optically anisotropic suspensions of nonspheroidal bioparticles, such as blood. As Fermat rays or geodesics enter the suspension, they evolve into a bundle of random paths or trajectories due to scattering by the suspended bioparticles. Overall, this can be interpreted as a bundle of Markov trajectories traced out by a "gas" of Brownian-like point photons being scattered and absorbed by the homogeneous distribution of uncorrelated cells in suspension. By considering the cumulative vectorial intersections of a statistical bundle of random trajectories through sets of interior data planes in the space containing the medium, the effective equivalent information content and behavior of the (generally unknown) analytical flux solutions of the radiative transfer equation rapidly emerges. The fluxes match the analytical diffuse flux solutions in the diffusion limit, which verifies the accuracy of the algorithm. The method is not constrained by the diffusion limit and gives correct solutions for conditions where diffuse solutions are not viable. Unlike conventional Monte Carlo and numerical techniques adapted from neutron transport or nuclear reactor problems that compute scalar quantities, this vectorial technique is fast, easily implemented, adaptable, and viable for a wide class of biophotonic scenarios. By comparison, other analytical or numerical techniques generally become unwieldy, lack viability, or are more difficult to utilize and adapt. Illustrative calculations are presented for blood medias at monochromatic wavelengths in the visible spectrum. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 27
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6552-6572 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A criterion for the emergence of new eigenvalues is found for the linear scattering problem associated with the Benjamin–Ono (BO) equation. This bifurcation occurs due to perturbations of nongeneric potentials which include the soliton solutions of the BO equation. The asymptotic approximation of an exponentially small new eigenvalue is derived. The method is based on the expansion of a localized function through a complete set of unperturbed eigenfunctions. Explicit expressions are obtained for the soliton potentials. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 28
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6607-6630 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider the initial value problem of the relativistic Euler equations when the underlying space–time is not flat but conformally flat, and demonstrate existence of solutions with shocks, with time-independent bounds, in some cases from big bang till big crunch. Our theorem requires that the space–time metric satisfy certain bounds, but these do not constrain the curvature of space–time, and hence our theorem may guarantee uniform bounds on solutions until the formation of curvature singularities. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 29
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6651-6667 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The circularity property of stationary-axisymmetric asymptotically flat solutions of the coupled Einstein conformally invariant scalar field equations is investigated. It is proven that as a result of the coupling of the scalar field to the background scalar curvature, in general such solutions fail to be circular. Consequently, it is argued that the space of stationary, black hole equilibrium states may contain states which are not circular. However, the circular stationary-axisymmetric sector is nonempty and in fact it is proven that: All circular, stationary-axisymmetric asymptotically flat black hole solutions are those and only those black holes states described by the two parameter family of Kerr black holes. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 30
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6696-6705 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The space–time disclination is studied by making use of the decomposition theory of gauge potential in terms of the antisymmetric tensor field and φ-mapping method. It is shown that the self-dual and anti-self-dual parts of the curvature compose the space–time disclinations which are classified in terms of topological invariants—winding number. The projection of space–time disclination density along an antisymmetric tensor field is quantized topologically and characterized by Brouwer degree and Hopf index. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 31
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2367-2401 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The coregular real representations of the compact simple Lie groups are classified and the equalities and inequalities defining their orbit spaces are determined in the case of 2, 3 and 4 basic polynomial invariants. The results are obtained making use of the classification of the complex coregular simple Lie groups given by G. W. Schwarz and of the determination of all the allowable metric matrices for q-dimensional (q≤4) orbit spaces of compact coregular linear groups, recently obtained by the present authors. The results are used to determine in a rigorous way the minima of two SO(10) and E6 invariant Higgs potentials. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 32
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5199-5230 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider quantum dynamical systems whose degrees of freedom are described by N×N matrices, in the planar limit N→∞. Examples are gauge theories and the M(atrix)-theory of strings. States invariant under U(N) are "closed strings," modeled by traces of products of matrices. We have discovered that the U(N)-invariant operators acting on both open and closed string states form a remarkable new Lie algebra which we will call the heterix algebra. (The simplest special case, with one degree of freedom, is an extension of the Virasoro algebra by the infinite-dimensional general linear algebra.) Furthermore, these operators acting on closed string states only form a quotient algebra of the heterix algebra. We will call this quotient algebra the cyclix algebra. We express the Hamiltonian of some gauge field theories (like those with adjoint matter fields and dimensionally reduced pure QCD models) as elements of this Lie algebra. Finally, we apply this cyclix algebra to establish an isomorphism between certain planar matrix models and quantum spin chain systems. Thus we obtain some matrix models solvable in the planar limit; e.g., matrix models associated with the Ising model, the XYZ model, models satisfying the Dolan–Grady condition and the chiral Potts model. Thus our cyclix Lie algebra describes the dynamical symmetries of quantum spin chain systems, large-N gauge field theories, and the M(atrix)-theory of strings. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 33
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5268-5291 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A simple prescription allows us to transform, by appropriate complexification, any one-dimensional many-body problem (describing "motions on a line") with Newtonian ("acceleration equals forces") equations of motion featuring forces which depend analytically on the positions, and possibly on the velocities, of the particles, and which are moreover scaling- or translation-invariant, into a two-dimensional many-body problem (describing "motions in the plane") with rotation-invariant equations of motion. If the original (one-dimensional) model is Hamiltonian, the two-dimensional model is also Hamiltonian (in fact, bi-Hamiltonian). In this manner, starting from known integrable or solvable one-dimensional many-body problems, integrable or solvable many-body problems in the plane, generally featuring much richer dynamics, are obtained. Several examples are exhibited. Finally another, more direct, prescription is outlined, to transform by complexification almost any one-dimensional many-body problem into a rotation-invariant many-body problem in the plane. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 34
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 1142-1152 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We introduce the new nonhomogeneous graded matrix algebra Matn(R) over the ring R of the pseudodifferential operators of the arbitrary orders. This algebra forms the generalization of the algebra of the standard matrix pseudodifferential operators. We show that the Matn(R) algebra admits the nontrivial central extension. The case n=2 is considered in some detail. As the example we consider the Mat2(W1+∞), Mat2(Virasoro) and Mat2(sl(2,C)) algebras. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 35
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 1223-1235 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The configuration space of a system of n particles has the structure of a principal fiber bundle under the action of the rotation group. In this paper, identities are derived for the curvature of the natural connection on this bundle. These identities are translated into statements about the Coriolis tensor, the local expression for this curvature on the base space of the bundle. The Coriolis tensor is shown to obey field equations of the Yang–Mills type. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 36
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 695-703 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A one-parameter deformation of Calogero–Moser quantum problem is introduced. It is shown that corresponding Schrödinger operator is integrable for any value of the parameter and algebraically integrable in case of integer value. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 37
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 683-694 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We discuss hypersurface motions in Riemannian manifolds whose normal velocity is a function of the induced hypersurface volume element and derive a second-order partial differential equation for the corresponding time function τ(x) at which the hypersurface passes the point x. Equivalently, these motions may be described in a Hamiltonian formulation as the singlet sector of certain diffeomorphism-invariant field theories. At least in some (infinite class of) cases, which could be viewed as a large-volume limit of Euclidean M-branes moving in an arbitrary M+1-dimensional Riemannian manifold, the models are integrable: In the time-function formulation the equation becomes linear [with τ(x) a harmonic function on the embedding Riemannian manifold]. We explicitly compute solutions to the large volume limit of Euclidean membrane dynamics in R3 by methods used in electrostatics and point out an additional gradient flow structure in Rn. In the Hamiltonian formulation we discover infinitely many hierarchies of integrable, multidimensional, N-component theories possessing infinitely many diffeomorphism invariant, Poisson commuting, conserved charges. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 38
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5952-5963 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The one-dimensional circle map is frequently used to model the quasiperiodic route to chaos. In this paper we study the transition to criticality for circle maps with a golden mean winding number in the limit as the order of the map inflection point N=1+ε approaches unity. The solution to the relevant pair of functional equations consists of the subcritical solution together with a perturbative correction of order ε. We derive functional relations that the perturbative correction must satisfy and produce numerical evidence that these equations are indeed satisfied. A similar analysis is performed for the golden mean eigenvalue equations. Power law conjugacy of the subcritical solution to order N=1+ε enables us to obtain a closed form solution for the perturbative correction that satisfies the constraint relations exactly. This is compared with the more interesting critical case associated with a circle map whose inflection point is infinitesimally close to unity. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 39
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6040-6050 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Chaos in Robertson–Walker cosmological models where gravity is coupled to one or more scalar fields has been studied by a few authors, mostly using numerical simulations. In this paper we begin a systematic study of the analytical aspect. We consider one conformally coupled scalar field and, using the fact that the model is integrable when the field is massless, we show in detail how homoclinic chaos arises for nonzero masses using a perturbative method. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 40
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6066-6085 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: After dimensional reduction the stationary sector of SO(3) symmetric Einstein's gravity is identified with an SL(2,R)/SO(2) Sigma model coupled to a one-dimensional gravitational remnant. The space of classical solutions consists of the Schwarzschild and Taub–NUT family. A Dirac quantization of this system is performed and the observables—the mass and the charge operator—are shown to be self-adjoint operators with a continuous spectrum ranging from −∞ to ∞. The Hilbert space is constructed explicitly using a harmonic space approach. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 41
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6162-6174 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This work is devoted to the establishment of a Poisson structure for a format of equations known as generalized Lotka–Volterra systems. These equations, which include the classical Lotka–Volterra systems as a particular case, have been deeply studied in the literature. They have been shown to constitute a whole hierarchy of systems, the characterization of which is made in the context of simple algebra. Our main result is to show that this algebraic structure is completely translatable into the Poisson domain. Important Poisson structures features, such as the symplectic foliation and the Darboux canonical representation, rise as a result of rather simple matrix manipulations. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 42
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6225-6240 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper the algebraic expressions for SO(N) Racah coefficients involving the coupling of three irreducible representations (1 0(overdot)), (m1 m2 m3 0(overdot)) and (1 0(overdot)) are given by using the building-up process. Their properties are discussed in detail. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 43
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6242-6242 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 44
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5123-5147 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A fermion realization of the nuclear Sp(6,R) model, which complements the traditional bosonic representation, is developed. A recursive process is presented in which symplectic matrix elements of arbitrary one-body fermion operators between states of excitation N(h-dash-bar)ω and N′(h-dash-bar)ω in the same or in different symplectic bands are related back to valence shell matrix elements, which can be evaluated by standard shell model techniques. Matrix elements so determined may be used to calculate observables such as electron scattering form factors which carry detailed structural information on nuclear wave functions. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 45
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 355-362 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The billiard system within an ellipsoid in three-dimensional space is considered. We describe periodical trajectories of that mechanical system deriving analytical condition of Cayley's type for generalized Poncelet's theorem, using methods of algebrogeometric integration.© 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 46
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 372-379 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The theory of distributions in non-Riemannian spaces is used to obtain exact static thin domain wall solutions of Einstein-Cartan equations of gravity. Curvature δ-singularities are found while Cartan torsion is given by Heaviside functions. Weitzenböck planar walls are characterized by torsion δ-singularities and zero curvature. It is shown that Weitzenböck static thin domain walls do not exist exactly as in general relativity. The global structure of Weitzenböck nonstatic torsion walls is investigated. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 47
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 467-488 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new technique, the double-induced technique, is introduced for constructing irreducible symmetry operators (ISO's) adapted to the group chain G⊃G(s). Simple algebraic expressions of irreducible matrices, the ISO's and symmetry adapted functions (SAF's) are derived for the group chain T⊃C3 for both single-valued and double-valued representations in a unified way. The simplicity of the results lies in the fact that the ISO's and SAF's are functions of only the quatum numbers of the group chain [the analogy of (j,m) for the group chain SO3⊃SO2], without involving any irreducible matrix elements. The symmetries of the SAF's are disclosed for the first time. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 48
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6537-6546 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider the Gyldén problem—a perturbation of the Kepler problem via an explicit function of time. For certain general classes of planar periodic perturbations, after proving a Poincaré–Melnikov-type criterion, we find a manifold of orbits in which the dynamics is given by the shift automorphism on the set of bi-infinite sequences with infinitely many symbols. We achieve the main result by computing the Melnikov integral explicitly. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 49
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6631-6650 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The notion of center of mass for an isolated system has been previously encoded in the definition of the so-called nice sections. In this article we present a generalization of the proof of existence of solutions to the linearized equation for nice sections, and formalize a local existence proof of nice sections relaxing the radiation condition. We report on the differentiable and non-self-crossing properties of this family of solutions. We also give a proof of the global existence of nice sections. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 50
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5762-5771 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The rational conformal field theory extensions of W1+∞ at c=1 are in one-to-one correspondence with one-dimensional integral lattices L(m). Each extension is associated with a pair of oppositely charged "vertex operators" of charge square m∈N. Their product defines a bilocal field Vm(z1,z2) whose expansion in powers of z12=z1−z2 gives rise to a series of (neutral) local quasiprimary fields Vl(z,m) (of dimension l+1). The associated bilocal exponential of a normalized current generates the W1+∞ algebra spanned by the Vl(z,1) (and the unit operator). The extension of this construction to higher (integer) values of the central charge c is also considered. Applications to a quantum Hall system require computing characters (i.e., chiral partition functions) depending not just on the modular parameter τ, but also on a chemical potential ζ. We compute such a ζ dependence of orbifold characters, thus extending the range of applications of a recent study of affine orbifolds. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 51
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5789-5797 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We present several examples of quasiexactly solvable N-body problems in one, two, and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding polynomials form an orthogonal set, and many of their properties are similar to those of the Bender–Dunne polynomials. We also discuss QES problems where the polynomials do not form an orthogonal set. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 52
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5870-5893 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The problem of the electromagnetic field created by a thin, straight conductor of infinite length carrying a forward traveling-wave current with a complex propagation constant γ above a homogeneous and isotropic planar earth of wave number k1 is formulated in terms of contour integrals. In the limit where γ becomes equal to the free-space wave number k0, the component of the magnetic field in air normal to both conductor and interface is evaluated in closed form in terms of known special functions while the remaining components of the field in air are expressed as series expansions in δ=k02(k14−k04)−1/2 via the application of a contour integration technique. The new analytical formulas involve familiar transcendental functions and are valid at any distance from the source. The analysis sheds light on the intricate nature of low-frequency electromagnetic fields generated by transmission lines in the presence of a conducting or a dielectric half-space. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 53
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5925-5933 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We use Kepler's eccentric anomaly in order to get explicit equations for the planetary orbits in a solar system. By successively modifying the corresponding Lagrangian, we build a Lagrangian for a relativistic two-body problem, the trajectories of which are conics in Minkowski space. The equations of these trajectories, projected on a three-space, exhibit new anomalies. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 54
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5946-5951 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using the quantum inverse scattering method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six-vertex model with reflecting end. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 55
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6001-6010 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Cauchy horizons are shown to be differentiable at end points where only a single null generator leaves the horizon. A Cauchy horizon fails to have any null generator end points on a given open subset iff it is differentiable on the open subset and also iff the horizon is (at least) of class C1 on the open subset. Given the null convergence condition, a compact horizon which is of class C2 almost everywhere has no end points and is (at least) of class C1 at all points. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 56
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 380-400 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For a rotating dust with a 3-dimensional symmetry group all possible metric forms can be classified and, within each class, explicitly written out. This is made possible by the formalism of Plebanski based on the Darboux theorem. In the resulting coordinates, the Killing vector fields (if any exist) assume a special form. Each Killing vector field may be either spanned on the fields of velocity and rotation or linearly independent of them. By considering all such cases one arrives at the classification. With respect to the structures of the groups, this is just the Bianchi classification, but with all possible orientations of the orbits taken into account. In this paper, which is part 1 of a 3-part series, all solutions are considered for which two Killing fields are spanned on velocity and rotation. The solutions of Lanczos and Gödel are identified as special cases, and their new invariant definitions are provided. In addition, a new invariant definition is given of the Ozsvath class III solution. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 57
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 401-422 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This is the second part of a series of 3 papers. Using the same method and the same coordinates as in part 1, rotating dust solutions of Einstein's equations are investigated that possess 3-dimensional symmetry groups, under the assumption that only one of the Killing fields is spanned on the fields of velocity uα and rotation wα, while the other two define vectors that are linearly independent of uα and wα at every point of the spacetime region under consideration. The Killing fields are found and the Killing equations solved for the components of the metric tensor in every case that arises. The Einstein equations are simplified in a few cases, three (most probably) new solutions are found, and several classes of solutions known earlier are identified in the present scheme. They include those by Ozsváth, Maitra, Ellis, King, and Vishveshwara and Winicour. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 58
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 454-466 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper new exact solutions for the Dirac equation are presented for the case of a particle in tensor wave field on the background of gravitation. Consideration is given to different configurations introducing the tensor interaction, which result in the required separation of variables by the algebraic method and lead to the derivation of exact solutions for the Dirac equation in the corresponding field situation. At the same time, most general metrics allowing for the exact solutions are given. The cases of zero and nonzero rest mass of a particle are with treated here. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 59
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5083-5097 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the leading corrections to the emergent canonical commutation relations arising in the statistical mechanics of matrix models, by deriving several related Ward identities, and give conditions for these corrections to be small. We show that emergent canonical commutators are possible only in matrix models in complex Hilbert space for which the numbers of fermionic and bosonic fundamental degrees of freedom are equal, suggesting that supersymmetry will play a crucial role. Our results simplify, and sharpen, those obtained earlier by Adler and Millard. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 60
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5292-5306 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two families of nonstandard two-dimensional Poisson structures for systems of Newton equations are studied. They are closely related either with separable systems or with the so-called quasi-Lagrangian systems. A theorem characterizing the general form of bi-Hamiltonian formulation for separable systems in two and in n dimensions is formulated and proved. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 61
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5307-5315 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A construction of a stochastic, Lagrangian path integral representation is presented for classical Green's functions or propagators for radiative transfer in random scattering medias. As Fermat rays comprising the initial collimated pulse (e.g., from a laser) enter the medium, they evolve into a bundle of random paths or trajectories due to scattering. Stochastically, this can be interpreted as a bundle of randomly evolving Markov trajectories traced out by a gas or ensemble of "Brownian-type" classical point photons undergoing multiple scatterings. The path integral is structurally of the same form as a Wick rotated Euclidean quantum Feynman integral with direct optical analogs of the Hamiltonian and Lagrangian emerging. However, the optical stochastic integral is real and is defined in real time becoming exponentially damped rather than oscillatory. The calculation also constitutes an alternative mathematical derivation of the time dependent diffusion equation from the radiative transfer theory. The limits of the path integral representation give a maximally diffused Gaussian distribution of the heat kernal form (the large scatter limit) and a Beer's law exponential decay corresponding to the extremal Fermat rays obeying Euler–Lagrange equations (the zero scatter limit). The approach also highlights the direct structural analogs between classical radiative transfer and optical diffusion in real time (t) and ordinary quantum mechanics in Euclidean time ((square root of)(−1)t=it). © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 62
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5364-5376 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: After embedding the Kadomtsev–Petviashvili equation in higher dimensions and extending the Painlevé analysis approach to a new form such that the coefficients of the expansion around the singular manifold possess conformal invariance and contain explicit new space variables, we can get infinitely many Painlevé integrable models in (3+1)-dimensions and higher dimensions. Some concrete higher dimensional modified Korteweg–de Vries type of extensions are given. Whether the models are Lax integrable or integrable under other meanings remain still open. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 63
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5377-5395 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general approach to constructing the polynomial solutions satisfying various reductions of the Kadomtsev–Petviashvili (KP) hierarchy is described. Within this approach, the reductions of the KP hierarchy are equivalent to certain differential equations imposed on the τ-function of the hierarchy. In particular, the l-reduction and the k-constraint as well as their generalized counterparts are considered. A general construction of the rational solutions to these reductions is found and the particular solutions are explicitly derived for some typical examples including the KdV and Gardner equations, the Boussinesq and classical Boussinesq systems, the NLS and Yajima–Oikawa equations. It is shown that the degenerate rational solutions of the KP hierarchy are related to stationary manifolds of the Calogero–Moser (CM) hierarchy of dynamical systems. The scattering dynamics of interacting particles in the CM systems may become complicated due to an anomalously slow fractional-power rate of the particle motion along the stationary manifolds. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 64
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4284-4298 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We extend previous work on the algebraic first-order moments of polarization profiles of hydrogen lines in the presence of external fields, to include the effect of configuration mixing induced by the applied fields. An algebraic formula for hydrogen line shifts due to the quadratic Stark effect is derived, under the assumption that the applied electric field is weak enough that line quenching induced by field ionization can be neglected. The derivation of such a formula is made possible by an aimed use of standard techniques of projection-operator algebra and of the fundamental implications of the spectral theorem. The results of this paper should help in decreasing the amount of numerical work needed in the calculation of line shifts of hydrogen lines induced by the presence of electric fields, as the preliminary numerical calculation of the Hamiltonian eigenvalues and eigenvectors is avoided, thus making calculations tractable for lines of higher hydrogen series than considered so far, e.g., in applications of pressure-broadening theory. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 65
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4369-4416 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider Schrödinger operators of the form Hλ=−Δ+V+λW on L2(Rν) (ν=1, 2, or 3) with V periodic, W short range, and λ a real non-negative parameter. Then the continuous spectrum of Hλ has the typical band structure consisting of intervals, separated by gaps. In the gaps there may be discrete eigenvalues of Hλ that are functions of the parameter λ. Let (a,b) be a gap and E(λ)∈(a,b) an eigenvalue of Hλ. We study the asymptotic behavior of E(λ) as λ approaches a critical value λ0, called a coupling constant threshold, at which the eigenvalue either emerges from or is absorbed into the continuous spectrum. A typical question is the following: Assuming E(λ)↓a as λ↓λ0, is E(λ)−a∼c(λ−λ0)α for some α〉0 and c≠0, or is there an expansion in some other quantity? As one expects from previous work in the case V=0, the answer strongly depends on ν. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 66
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4540-4545 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The one-loop effective potential of a thermodynamic fermion loop in a constant magnetic field is studied. As expected, it can be interpreted literally as a discretized sum of (D−2)-dimensional energy density above the Dirac sea. Large/small mass expansions of the potential are also examined. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 67
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4016-4040 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Gaussian signals play a very special role in classical time–frequency analysis because they are solutions of apparently unrelated problems such as minimum uncertainty, and positivity and separability of Wigner–Ville distributions. We investigate here some of the logical connections which exist between these different features, and we discuss some examples and counterexamples of their extension to more general joint distributions within Cohen's class and the affine class. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 68
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4165-4194 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we study the time evolution for the Schrödinger equation and the wave equation on the line when the interaction term is a fractal measure. First, we extend the usual one-dimensional potential scattering formalism to interactions defined as measures. Then we show how to retrieve information on the fractality of the interaction term from time-dependent scattering data. In the case of the Schrödinger equation we shall obtain the wavelet correlation dimension of the scatterer. For the wave equation the whole set of generalized multifractal dimensions can be recovered, provided the scatterer actually is fractal (nonsmooth). In this latter case, we also show how the reflected wave packets can be interpreted in terms of wavelet transform of the interaction. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 69
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4213-4225 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Given any self-similar quasicrystal Λ in Rn with inflation θ〉1, we construct bases of L2(Rn) having the following structure: θnj/2ψλ(θjx−λ), λ∈Λ(backward-slash)θΛ, j∈Z, where the mother wavelets ψλ, λ∈Λ(backward-slash)θΛ, are smooth and with exponential decay or compact support. We also show that wavelets ψλ constitute a relatively compact set in some Sobolev space and that they depend continuously on λ when Λ is equipped with an appropriate topology. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 70
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4226-4245 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper concerns square wave analysis, which is in no small part a generalization of the Fourier analysis based on sine and cosine functions. Following sine and cosine functions square waves become another frequently used and easily generated waveform in electronics, so it is an urgent practical problem to study the basic properties of square waves and the fundamental theory of square wave analysis. Like the sine-cosine function system, the square wave system, i.e., the function system of square waves with different frequencies (or periods), is linearly independent and complete in the real Hilbert spaces L2(−π,π), so square waves can approximate an arbitrary quadratically integrable function with a vanishing mean-square error. Since the square wave system is nonorthogonal, its biorthogonal functions are presented so that a function with a certain condition can be expanded as a square wave series easily. Meanwhile the orthogonalization of the square wave system is discussed so that a quadratically integrable function can be approximated best by a superposition of finite square waves. These results form the theory basis of the square wave analysis technique in modern electronics. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 71
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4773-4784 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We construct the supersymmetric extensions of the Darboux–Bäcklund transformations (DBTs) for the Manin–Radul super Korteweg–de Vries (KdV) hierarchy using the super-pseudo-differential operators. The elementary DBTs are triggered by the gauge operators constructed from the wave functions and adjoint wave functions of the hierarchy. Iterating these elementary DBTs, we obtain not only Wronskian-type but also binary-type superdeterminant representations of the solutions. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 72
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4849-4873 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We establish the existence of hairy black holes in su(N) Einstein–Yang–Mills theories, described by N−1 parameters, corresponding to the nodes of the gauge field functions. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 73
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4874-4890 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Dirac fermion fields associated with different tetrad gravitational fields and under general covariant transformations are described by sections of the composite bundle S→Σ→X4, which is both the Dirac spinor bundle over the tetrad bundle Σ and the natural one over X4. As a natural bundle, S→X4 admits general covariant transformations which are those of Dirac spin structures. A different way is to consider a background spin structure. We find gauge transformations which preserve this spin structure, but act on effective tetrad fields as general covariant transformations. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 74
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3522-3529 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Applying the doublet representation we analyze the solutions of a Hamiltonian system which has eigenstates with complex eigenvalues. The example of the Friedrichs model allows us to show how the appearance of solutions with non-Hilbert initial conditions is linked to the energy degeneration of the Hamiltonian spectrum. We discuss the difficulties of giving a physical meaning to the growing or decaying non-Hilbert solutions. We also suggest a way to circumvent the problem of the anomalous probabilities related to both complex energy eigenvalues and degeneration of the spectrum. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 75
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3765-3771 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that a class of important integrable nonlinear evolution equations in (2+1) dimensions can be associated with the motion of space curves endowed with an extra spatial variable or equivalently, moving surfaces. Geometrical invariants then define topological conserved quantities. Underlying evolution equations are shown to be associated with a triad of linear equations. Our examples include Ishimori equation and Myrzakulov equations which are shown to be geometrically equivalent to Davey-Stewartson and Zakharov-Strachan (2+1) dimensional nonlinear Schrödinger equations, respectively. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 76
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3916-3926 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In physical geodesy one considers several (exterior) Robin boundary value problems for the Laplace equation in three dimensions. The ellipsoidal Stokes problem, which occurs in context of gravimetric determination of the geoid, belongs to this class. Up to now, this and related problems have been treated with high order series expansions of spherical and spheroidal harmonics. In this article we investigate the nullfield method for this class of boundary value problems. An integral equation formulation is achieved, and existence and uniqueness conditions are attained in view of the Fredholm alternative. For the case that the underlying surface is a triaxial ellipsoid or an oblate spheroid, explicit expressions for the eigenvalues and eigenfunctions for the boundary integral operator are provided. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 77
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3019-3030 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A concept of quantum martingale measure is introduced and examples are constructed as quantum stochastic spectral integrals in Fock space. These are then utilized as space–time noise to drive a parabolic stochastic partial differential equation (spde). We establish the existence and uniqueness of the solutions as families of densely defined closable operators in Fock space that are jointly continuous in time and space variables and satisfy a Markov property. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 78
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4071-4090 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f〉0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the associated Wigner function is given. Formulas expressing the basic operation (star-bracket) of the Lie algebra of symbols, which is isomorphic to that of the operators, are obtained. In addition, it is shown that the resulting calculus is covariant under a three-parameter group which contains the affine group as subgroup. This observation is the starting point of an investigation leading to a whole class of symbolic calculi which can be considered as modifications of the original one. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 79
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3828-3843 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A proof of the Poincaré–Birkhoff–Witt theorem is given for a class of generalized Lie algebras closely related to the Gurevich S-Lie algebras. As concrete examples, we construct the positive (negative) parts of the quantized universal enveloping algebras of type An and Mp,q,ε(n,K), which is a nonstandard quantum deformation of GL(n). In particular, we get, for both algebras, a unified proof of the Poincaré–Birkhoff–Witt theorem, and we show that they are genuine universal enveloping algebras of certain generalized Lie algebras. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 80
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3906-3915 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The purpose of this paper is to provide definitions for, and proofs of, the asymptotic formulas given by Edmonds, which relate the 3j and 6j symbols to rotation matrices. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 81
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 4201-4212 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: First an iterative process is described for subdivision and for scaling-up of the Penrose–Robinson tiles. Then we build the τ-wavelets of Haar (i.e., suitably normalized characteristic functions) on the tiles so that the orthogonality and multiresolution conditions are satisfied. Here τ=〈fraction SHAPE="CASE"〉12(1+5). © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 82
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3530-3546 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is known that in the Wentzel–Kramers–Brillouin approximation of multicomponent systems like the Dirac equation or Born–Oppenheimer approximation, an additional phase appears apart from the Berry phase. So far, this phase was only examined in special cases, or under certain restrictive assumptions, namely, that the eigenspaces of the matrix or endomorphism valued symbol of the Hamiltonian form trivial bundles. We give a completely global derivation of this phase which does not depend on any choice of local trivializing sections. This is achieved using a star product approach to quantization. Furthermore, we give a systematic and global approach to a reduction of the problem to a problem defined completely on the different "polarizations." Finally, we discuss to what extent it is actually possible to reduce the problem to a really scalar one, and make some comments on obstructions to the existence of global quasiclassical states. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 83
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 3577-3588 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We give the construction of quantum Lax equations for IRF models and the difference version of the Calogero–Moser–Sutherland model introduced by Ruijsenaars. We solve the equations using factorization properties of the underlying face Hopf algebras/elliptic quantum groups. This construction is in the spirit of the Adler–Kostant–Symes method and generalizes our previous work to the case of face Hopf algebras/elliptic quantum groups with dynamical R matrices. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 84
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2730-2747 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In a recent article, Alli and Sewell [J. Math. Phys. 36, 5598 (1995)] formulated a new version of the Dicke–Hepp–Lieb laser model in terms of quantum dynamical semigroups, and thereby extended the macroscopic picture of the model. In the present article, we complement that picture with a corresponding microscopic one, which carries the following new results. (a) The local microscopic dynamics of the model is piloted by the classical, macroscopic field, generated by the collective action of its components; (b) the global state of the system carries no correlations between its constituent atoms after transient effects have died out; and (c) in the latter situation, the state of the system at any time t maximizes its entropy density, subject to the constraints imposed by the instantaneous values of its macroscopic variables. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 85
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2781-2799 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We derive in this paper a generalized hydrodynamical model for semiconductors from a multicollision scale Boltzmann equation. We apply a Chapman–Enskog method for two time-scale collisional operators. These two time scales are linked respectively with the elastic part of the electron/lattice scattering term and the electron/electron collision term. Our model has a global entropy function and a symmetric formulation. It is a generalization of the classical hydrodynamical model since we add two terms: a "thermal friction force" and a "friction heat flux." Moreover, with some changes of parameters we obtain both the energy-transport model and the Euler–Poisson hydrodynamical model. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 86
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2859-2861 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The set of spinor equations linking the curvature spinors of a Riemann–Cartan space with the curvature spinors of the corresponding Riemann space is derived, and these are used to establish a simple relationship between Ψ-flat connections of the Riemann–Cartan space and Lanczos potentials of the Riemann space. This not only yields, very easily, a recent result of Bergqvist for the Kerr metric, but also enables Bergqvist's result to be generalized; specifically we show that a curvature-free connection, associated with a class of Kerr–Schild metrics, can be identified as a Lanczos potential for the Weyl conformal curvature spinor of these spaces. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 87
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 1919-1927 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling constants or temperatures. We are led to this after first developing the notion of partial supersymmetry, in which some, but not all, of the operators of a theory have superpartners, and using it to construct fermionic and parafermionic thermal partition functions, and to derive some number theoretic identities. In the process, we also find a bosonic analog of the Witten index, and use this, too, to obtain some number theoretic results related to the Riemann zeta function. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 88
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2077-2102 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We reformulate the theory of simple liquids in a field theoretical way by taking into account the triplet potential wijk, in addition to the external potential ui and the pair potential vij. The innovation here is the inversion method and the on-shell expansion which are the building blocks of a novel use of Legendre transformation developed in field theory. By the inversion method, we renormalize the theory in terms of one-, two-, and three-particle densities, and present a diagrammatic representation for a thermodynamical functional, which is the entropy except for a trivial constant, in terms of renormalized variables. In other words, we present an expression for the entropy in terms of only one-, two-, and three-particle densities: the n-particle density where n≥4 does not appear in the expression. The on-shell condition, which is a starting point of the on-shell expansion, of the thermodynamical functional thus obtained (the entropy) leads to a set of three self-consistent equations for one-, two-, and three-particle densities. Through one of the self-consistent equations, we can systematically improve the Kirkwood's superposition approximation for the three-particle density. The on-shell conditions for other thermodynamical functionals, also obtained in this article, are found to be extentions of various well-known equations in the theory of simple liquids. The formulation presented here is complementary to the conventional re-summation techniques for renormalization of diagrams. In the present formulation, we do not have to care about the topological structure of diagrams, often characterized by the irreducibility of diagrams. Instead, by a perturbative calculation, we can automatically single out the diagrams with the topological structure predicted by the re-summation techniques. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 89
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2122-2140 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using a moving space curve formalism, geometrical as well as gauge equivalence between a (2+1) dimensional spin equation (M-I equation) and the (2+1) dimensional nonlinear Schrödinger equation (NLSE) originally discovered by Calogero, discussed then by Zakharov and recently rederived by Strachan, have been estabilished. A compatible set of three linear equations are obtained and integrals of motion are discussed. Through stereographic projection, the M-I equation has been bilinearized and different types of solutions such as line and curved solitons, breaking solitons, induced dromions, and domain wall type solutions are presented. Breaking soliton solutions of (2+1) dimensional NLSE have also been reported. Generalizations of the above spin equation are discussed. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 90
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2193-2200 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In the modern version of 5-D general relativity where the fifth dimension induces matter in 4-D space–time, a choice of coordinates and its restrictions on the geometry (a gauge) dictates the physics of the gravitational, electromagnetic, and scalar fields (spin 2, 1, 0). We extend previous work by concentrating on two related problems. First, we use the lapse and shift formalism to carry out a (4+1) split of Kaluza–Klein theory valid in any gauge. Second, we use a conformal gauge to simplify the 5-D field equations, find a plane-wave solution, and identify the energy and momentum of the particle associated with it. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 91
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2682-2692 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper presents some methods of representing canonical commutation relations in terms of hyperfinite-dimensional matrices, which are constructed by nonstandard analysis. The first method uses representations of a nonstandard extension of the finite Heisenberg group, called hyperfinite Heisenberg group. The second is based on hyperfinite-dimensional representations of so(3). Then, the cases of infinite degree of freedom are argued in terms of the algebra of hyperfinite para-Fermi oscillators, which is mathematically equivalent to a hyperfinite-dimensional representation of so(n). © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 92
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2808-2812 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A model for the 2×2 AKNS system is extended for the two-block AKNS system. Zeroes of the determinant of the J-diagonal scattering matrix blocks give the bound states of such a system. The couple coefficients are now matrices. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 93
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2800-2807 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A Dispersive Wave equation in 2+1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave equation (GLDW). Using Singularity Analysis and techniques based upon the Painlevé Property leading to the Double Singular Manifold Expansion we shall find the Miura Transformation which converts the 2LDW equation into the GLDW equation. Through this Miura transformation we shall also present the Lax pair of the 2LDW equation as well as some interesting reductions to several already known integrable systems in 1+1 dimensions. As the 2LDW equation arises from a Miura transformation we propose that it should be treated conventionally as a Modified Equation. In this case, we propose its designation as The MGLDW Equation. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 94
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2325-2332 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider the problems of minimizing and maximizing the gap between the two lowest Dirichlet eigenvalues of the Schrödinger operator −Δ+V(x) on a bounded domain in Rn, when the potential V is subjected to a p-norm constraint. We give characterization theorems for extremizing potentials. We prove in particular that a second eigenvalue corresponding to a minimizing potential is always single. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 95
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 1555-1565 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We apply recent results in the theory of PDE, specifically in problems with two different time scales, to Einstein's equations near their Newtonian limit. The results imply a justification to post-Newtonian approximations when initialization procedures to different orders are made on the initial data. We determine up to what order initialization is needed in order to detect the contribution to the quadrupole moment due to the slow motion of a massive body as distinct from initial data contributions to fast solutions and prove that such initialization is compatible with the constraint equations. Using the results mentioned, the first post-Newtonian equations and their solutions in terms of Green's functions are presented in order to indicate how to proceed in calculations with this approach. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 96
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2848-2858 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The r-matrix method and the method of separation of variables for restricted flows with Neumann constraints are considered. Restricted Jaulent–Miodek flows are taken as illustrative examples. Lax representations are obtained from the adjoint representation of the corresponding soliton hierarchy; the r-matrix formula, based on this Lax representation, is derived; and the separation of variables for the Hamilton–Jacobi equation are performed. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 97
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2866-2888 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A multidimensional cosmological model describing the evolution of (n+1) Einstein spaces in the theory with several scalar fields and forms is considered. When a (electro-magnetic composite) p-brane ansatz is adopted the field equations are reduced to the equations for the Toda-like system. The Wheeler–De Witt equation is obtained. In the case when n "internal" spaces are Ricci-flat, one space M0 has a non-zero curvature, and all p-branes do not "live" in M0; the classical and quantum solutions are obtained if certain orthogonality relations on parameters are imposed. Spherically symmetric solutions with intersecting non-extremal p-branes are singled out. A non-orthogonal generalization of intersection rules corresponding to (open, closed) Toda lattices is obtained. A chain of bosonic D≥11 models (that may be related to hypothetical higher dimensional supergravities and F-theories) is suggested. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 98
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 760-776 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This is the continuation of notes written for the NATO-ASI conference in Il Ciocco (September 96) consisting of the analysis of the links between estimating the splitting between the two first eigenvalues for the Schrödinger operator H and the proof of infrared estimates for quantities attached to Gaussian-type measures. These notes were mainly reporting on the "old" contributions of Dyson, Fröhlich, Glimm, Jaffe, Lieb, Simon, and Spencer (in the 1970s) in connection with more recent contributions of Pastur, Khoruzhenko, Barbulyak, and Kondrat'ev which treat in general more sophisticated models. Here we concentrate on the simplest model related to field theory and extend the results of Barbulyak and Kondrat'ev by mixing ideas coming from Pastur and Khozurenko related to the use of Bogolyubov's inequality with classical inequalities due to Ginibre, Lebowitz, Sokal, and others, or, in the case when the temperature T is zero, by applying rather elementary estimates on Schrödinger operators, in order to find lower bounds for second-order moments attached to the measure φ(functional relationship right)Trφ exp−βH/Tr exp−βH with β=1/T. This question was "left to the reader" in lectures given by J. Fröhlich in 1976 [Acta Phys. Austriaca, Suppl. XV, 133–269 (1976)], but we think that it is worthwhile to do this "homework" carefully. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 99
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 976-985 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The self-dual Yang–Mills equation in the (2+1)-dimensional space–time is considered. Binary Darboux transformation of a new kind is applied to obtain the infinite hierarchy of solutions expressed through ones of corresponding Lax pairs on an initial solution of the equation studied. Sufficient conditions are given for the solutions built to take values in the class of unimodular positive-definite matrices. A new infinitesimal Darboux transformation is introduced and a particular solution of the linearization of the self-dual Yang–Mills equation is given. Two hierarchies of infinitesimal symmetries depending on a solution of the nonlinear equation are extracted. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 100
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 6276-6290 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) symmetry allows a unified description of electrodynamics and general relativity as a classical gauge theory. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...