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  • American Chemical Society  (24,715)
  • American Institute of Physics (AIP)  (10,194)
  • 2000-2004  (34,909)
  • 1950-1954
  • 2001  (34,909)
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  • 2000-2004  (34,909)
  • 1950-1954
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  • 1
    Electronic Resource
    Electronic Resource
    Noncanonical quantization of gravity. II. Constraints and the physical Hilbert space (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4440-4465 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The program of quantizing the gravitational field with the help of affine field variables is continued. For completeness, a review of the selection criteria that singles out the affine fields, the alternative treatment of constraints, and the choice of the initial (before imposition of the constraints) ultralocal representation of the field operators is initially presented. As analogous examples demonstrate, the introduction and enforcement of the gravitational constraints will cause sufficient changes in the operator representations so that all vestiges of the initial ultralocal field operator representation disappear. To achieve this introduction and enforcement of the constraints, a well characterized phase space functional integral representation for the reproducing kernel of a suitably regularized physical Hilbert space is developed and extensively analyzed. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1385375
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  • 2
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    False vacuum decay: Effective one-loop action for pair creation of domain walls (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3292-3298 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An effective one-loop action built from the soliton field itself for the two-dimensional (2D) problem of soliton pair creation is proposed. The action consists of the usual mass term and a kinetic term in which the simple derivative of the soliton field is replaced by a covariant derivative. In this effective action the soliton charge is treated no longer as a topological charge but as a Noether charge. Using this effective one-loop action, the soliton–antisoliton pair production rate Γ/L=A exp[−S0] is calculated and one recovers Stone's exponential factor S0 and the prefactor A of Kiselev, Selivanov, and Voloshin. The results are also valid straightforwardly to the problem of pair creation rate of domain walls in dimensions D≥3. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1380442
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  • 3
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    On completeness of random exponentials in the Bargmann–Fock space (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3754-3768 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the completeness/incompleteness properties of a system of exponentials EΛ={eπλz; λ∈Λ}, viewed as elements of the Bargmann–Fock space of entire functions. We assume that the index set Λ is a realization of a random point field in C (the support of a random measure). We prove that the properties are determined by the density of the field, i.e., by the mean number of the field points per unit area. We also discuss certain implications and motivations of our results, in particular, the jumps of the integrated density of states of the Landau Hamiltonian with the random potential, equal to the sum of point scatters. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1379311
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  • 4
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    Unitary irreducible representations of a Lie algebra for matrix chain models (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3817-3838 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way. Moreover, they are the only states with a finite number of non-zero quantum numbers with respect to a certain set of maximally commuting linearly independent quantum observables. Any other state is a tensor product of a multiple meson state and a state coming from a representation of a quotient algebra that extends and generalizes the Virasoro algebra. We expect the representation theory of this quotient algebra to describe physical systems at the thermodynamic limit. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1384866
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  • 5
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    Invariant integration on classical and quantum Lie supergroups (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3871-3897 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Invariant integrals on Hopf superalgebras, in particular, the classical and quantum Lie supergroups, are studied. The uniqueness (up to scalar multiples) of a left integral is proved, and a Z2-graded version of Maschke's theorem is discussed. A construction of left integrals is developed for classical and quantum Lie supergroups. Applied to several classes of examples the construction yields the left integrals in explicit form. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1364689
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  • 6
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    Trefoil symmetry III. The full clover extension (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3947-3964 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We aim to approach a trefoil symmetry involving (Z4×Z4;q)-graded parameters, multiplets of generators of integer spin 〈2 with naive dimensions in the interval [0,1]. The resulting full clover extension involves as particular subalgebras the minimal clover extensions previously obtained. We address the introduction of further scalar, dimensionless multiplets, and central charges. They could provide connections among external and internal symmetries, perhaps after some graded symmetry breaking. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1383560
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  • 7
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    Comment on "Uncertainty principle for proper time and mass" [J. Math. Phys 40, 1237 (1999)] (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3975-3977 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Kudaka and Matsumoto derive the uncertainty relation c2ΔmΔτ(approximate)h between the proper time τ and rest mass m of a material particle by adopting for the description of the particle the Lagrangian L=M(τ(overdot)−c−1−gμνx(overdot)μx(overdot)ν)+eAμ(x)x(overdot)μ, defined on the enlarged space (xμ,τ,M), where M is an additional dynamical variable. A key step in the derivation of their uncertainty relation is the identification of the variable M with the rest mass m. Adopting the point of view of variational analysis, we show that such an identification goes against the relativistic requirement of the path dependence of proper time. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1367329
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  • 8
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    Response to "Comment on ‘Uncertainty principle for proper time and mass' " [J. Math. Phys. 42, 3975 (2001)] (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3978-3979 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1367330
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  • 9
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    Noncommutative tachyons and K-theory (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2765-2780 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show that the relation between D-branes and noncommutative tachyons leads very naturally to the relation between D-branes and K-theory. We also discuss some relations between D-branes and K-homology, provide a noncommutative generalization of the ABS construction, and give a simple physical interpretation of Bott periodicity. In addition, a framework for constructing Neveu–Schwarz fivebranes as noncommutative solitons is proposed. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1377270
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  • 10
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    Fundamental strings in open string theory at the tachyonic vacuum (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2844-2853 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show that the world-volume theory on a D-p-brane at the tachyonic vacuum has solitonic string solutions whose dynamics is governed by the Nambu–Goto action of a string moving in (25+1) dimensional space–time. This provides strong evidence for the conjecture that at this vacuum the full (25+1) dimensional Poincaré invariance is restored. We also use this result to argue that the open string field theory at the tachyonic vacuum must contain closed string excitations. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1377037
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  • 11
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    Strings in AdS3 and the SL(2,R) WZW model. I: The spectrum (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2929-2960 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we study the spectrum of bosonic string theory on AdS3. We study classical solutions of the SL(2,R) WZW model, including solutions for long strings with nonzero winding number. We show that the model has a symmetry relating string configurations with different winding numbers. We then study the Hilbert space of the WZW model, including all states related by the above symmetry. This leads to a precise description of long strings. We prove a no-ghost theorem for all the representations that are involved and discuss the scattering of the long string. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1377273
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  • 12
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    Sigma model approach to string theory effective actions with tachyons (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2854-2871 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Motivated by recent discussions of actions for tachyon and vector fields related to tachyon condensation in open string theory we review and clarify some aspects of their derivation within the sigma model approach. In particular, we demonstrate that the renormalized partition function Z(T,A) of the boundary sigma model gives the effective action for massless vectors which is consistent with the string S-matrix and beta function, resolving an old problem with this suggestion in the bosonic string case at the level of the leading F2(dF)2 derivative corrections to Born–Infeld action. We give a manifestly gauge invariant definition of Z(T,A) in non-Abelian NSR open string theory and check that its derivative reproduces the tachyon beta function in a particular scheme. We also discuss the derivation of similar actions for tachyon and massless modes in closed bosonic and NSR (type 0) string theories. In the bosonic case the tachyon potential has the structure −T2e−T, but it vanishes in the NSR string case. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1376129
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  • 13
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    Finite N AdS/CFT correspondence for Abelian and non-Abelian orbifolds, and gauge coupling unification (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2915-2928 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Although the AdS/CFT correspondence is rigorous only for an infinite N→∞ stack of D3-branes, it can be fruitfully studied for finite N as a source of gauge structures and choices for chiral fermions and complex scalars which solve the hierarchy problem by a conformal fixed point. We emphasize orbifolds AdS5×S5/Γ where the resulting GFT has N=0 supersymmetry. The fact that the complex scalars are prescribed by the construction limits the possible spontaneous symmetry breaking. Both Abelian and non-Abelian Γ are illustrated by simple examples. An accurate sin2 θ in electroweak unification can be obtained, suggesting that this approach merits further study. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1374450
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  • 14
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    Brane-world Kaluza–Klein reductions and branes on the brane (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3048-3070 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We present a systematic study of a new type of consistent "brane-world Kaluza–Klein reduction," which describes fully nonlinear deformations of codimension one objects that arise as solutions of a large class of gauged supergravity theories in diverse dimensions, and whose world-volume theories are described by ungauged supergravities with-one half of the original supersymmetry. In addition, we provide oxidations of these ansätz which are in general related to sphere compactified higher dimensional string theory or M-theory. Within each class we also provide explicit solutions of brane configurations localized on the world-brane. We show that at the Cauchy horizon (in the transverse dimension of the consistently Kaluza–Klein reduced world-brane) there is a curvature singularity for any configuration with a non-null Riemann curvature or a nonvanishing Ricci scalar that lives in the world-brane. Since the massive Kaluza–Klein modes can be consistently decoupled, they cannot participate in regulating these singularities. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1377272
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  • 15
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    D=4 chiral string compactifications from intersecting branes (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3103-3126 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Intersecting Dp-branes often give rise to chiral fermions living on their intersections. We study the construction of four-dimensional chiral gauge theories by considering configurations of type II D(3+n)-branes wrapped on nontrivial n-cycles on T2n×(R2(3−n)/ZN), for n=1, 2, 3. The gauge theories on the four noncompact dimensions of the brane world-volume are generically chiral and nonsupersymmetric. We analyze consistency conditions (RR tadpole cancellation) for these models, and their relation to four-dimensional anomaly cancellation. Cancellation of U(1) gauge anomalies involves a Green–Schwarz mechanism mediated by RR partners of untwisted and/or twisted moduli. This class of models is of potential phenomenological interest, and we construct explicit examples of SU(3)×SU(2)×U(1) three-generation models. The models are nonsupersymmetric, but the string scale may be lowered close to the weak scale so that the standard hierarchy problem is avoided. We also comment on the presence of scalar tachyons and possible ways to avoid the associated instabilities. We discuss the existence of (meta)stable configurations of D-branes on 3-cycles in (T2)3, free of tachyons for certain ranges of the six-torus moduli. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1376157
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  • 16
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    Extended objects from warped compactifications of M theory (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3161-3170 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the massive spectrum of fully wrapped branes in warped M-theory compactifications, including regimes where these states are parametrically lighter than the Planck scale or string scale. We show that many such states behave classically as extended objects in the noncompact directions in the sense that their mass grows with their size as measured along the Poincare slices making up the noncompact dimensions. On the other hand, these states can be quantized in a nontrivial regime: in particular, their spectrum of excitations in a limited regime can be obtained by a warped Kaluza–Klein reduction from ten dimensions. We briefly discuss scattering processes and loop effects involving these states, and also note the possibility of an exponential growth in the number of bound states of these objects as a function of energy. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1373422
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  • 17
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    Dynamical topology change in M theory (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 3171-3187 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the topology change in M theory compactifications on Calabi–Yau three-folds in the presence of G flux (the four form field strength). In particular, we discuss vacuum solutions in strongly coupled heterotic string theory in which the topology change is inevitable within a single space–time background. For rather generic choices of initial conditions, the field equations drive the Kähler moduli outside the classical moduli space of a Calabi–Yau manifold. Consistency of the solution suggests that degenerate flop curves—just as wrapped M theory fivebranes—carry magnetic charges under the four form field strength. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1377038
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  • 18
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    On the observables describing a quantum reference frame (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2477-2489 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A reference frame F is described by the element g of the Poincaré group P which connects F with a given fixed frame F0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have to be considered as quantum observables. However, these observables are not compatible and some of them, namely the coordinates of the origin of F, cannot be represented by self-adjoint operators. Both these difficulties can be overcome by considering a positive-operator-valued measure on P, covariant with respect to the left translations of the group, namely a covariance system. We develop a construction procedure for this kind of mathematical structure. The formalism is also used to discuss the quantum observables measured with respect to a quantum reference frame. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1370395
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  • 19
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    Perturbation of a lattice spectral band by a nearby resonance (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2490-2506 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A soluble model of weakly coupled "molecular" and "nuclear" Hamiltonians is studied in order to exhibit explicitly the mechanism leading to the enhancement of fusion probability in case of a narrow near-threshold nuclear resonance. We, further, consider molecular cells of this type being arranged in lattice structures. It is shown that if the real part of the narrow nuclear resonance lies within the molecular band generated by the intercellular interaction, an enhancement, proportional to the inverse width of the nuclear resonance, is to be expected. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1371264
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    Symmetry transformations in extended irreversible thermodynamics (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2531-2539 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we consider symmetry transformations that preserve the first law and the second law of thermodynamics, as well as the pseudo-Riemannian structure of the Legendre manifold defined in terms of the second derivative matrix of the entropy function in extended irreversible thermodynamics. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1368844
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    On bidirectional fifth-order nonlinear evolution equations, Lax pairs, and directionally dependent solitary waves (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2567-2589 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper, Lax pairs are constructed for two fifth-order nonlinear evolution equations of "Boussinesq"-type which govern wave propagation in two opposite directions. One of the equations is related to the well-known Sawada–Kotera (SK) equation and, through its bilinear form, is identified with the Ramani equation. The second equation—about which very little seems to be known—may be considered a bidirectional version of the Kaup–Kupershmidt (KK) equation and is the main focus of this study. The "anomalous" solitary wave of this latter equation is derived and is found to possess the remarkable property that its profile depends on the direction of propagation. This type of directional dependence would appear to be quite unusual and, to our knowledge, has not been reported in the literature before now. By taking an appropriate undirectional (long wave) limit, it is shown that neither the Ramani, nor the bidirectional Kaup–Kupershmidt (bKK) equation can be classified as truly "Boussinesq" in character (a distinction that is made precise in the study). Recursion formulas are given for generating an infinity of conserved densities for both equations. These are used to obtain the first few conservation laws of the bKK and Ramani equations explicitly; not surprisingly, they exhibit the same lacunary behavior as their unidirectional counterparts. In conclusion, a canonical interpretation of the N-soliton solution of the bKK equation is proposed which provides a basis for constructing these anomalous solitons in a future work. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1354642
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    An operator valued extension of the super Korteweg–de Vries equations (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2625-2634 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An extension of the super Korteweg–de Vries (KdV) integrable system in terms of operator valued functions is obtained. Following the ideas of Gardner, a general algebraic approach for finding the infinitely many conserved quantities of integrable systems is presented. The approach is applied to the above described system and infinitely many conserved quantities are constructed. In a particular case they reduce to the corresponding conserved quantities of super KdV. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1368139
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    Casimir energy of a semi-circular infinite cylinder (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1974-1986 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Casimir energy of a semi-circular cylindrical shell is calculated by making use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symmetry axes of the cylinder and by considering only half of this configuration. All the surfaces, including the cutting plane, are assumed to be perfectly conducting. The zeta functions for scalar massless fields obeying the Dirichlet and Neumann boundary conditions on the semi-circular cylinder are constructed exactly. The sum of these zeta functions gives the zeta function for the electromagnetic field in question. The relevant plane problem is considered also. In all the cases the final expressions for the corresponding Casimir energies contain the pole contributions which are the consequence of the edges or corners in the boundaries. This implies that further renormalization is needed in order for the finite physical values for vacuum energy to be obtained for given boundary conditions. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1361064
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    Chaotic and irreversible properties of quantum scattering systems (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2023-2054 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Recent results for a free particle are generalized to N-particle quantum systems. Chaotic and irreversible behavior occurs in scattering states that belong to a certain Hilbert space K2 with a preferred time direction pointing to the future. At positive times the time evolution of positive observables exhibits quantum analogs of sensitive dependence on initial conditions, topological transitivity, and existence of a dense set of periodic points. A mixture of states in K2 can be described in terms of a density operator with thermodynamical entropy that increases to its least upper bound when the time tends to infinity. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1345872
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    k-cosymplectic manifolds and Lagrangian field theories (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2092-2104 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A geometrical description of classical field theories of first order is given. The underlying k-cosymplectic structure permits to derive the corresponding field equations. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1360997
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    Conformally flat anisotropic spheres in general relativity (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2129-2143 
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    Notes: The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic fluids. The slow evolution of these models is contrasted with the evolution of models with similar energy density or radial pressure distribution but nonvanishing Weyl tensor, thereby bringing out the different role played by the Weyl tensor, the local anisotropy of pressure, and the inhomogeneity of the energy density in the collapse of relativistic spheres. © 2001 American Institute of Physics.
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    Wave equations with point interactions in finite energy spaces (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2184-2202 
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    Notes: Given the abstract wave equation φ¨−Δαφ=0, where Δα is the Laplace operator with a point interaction of strength α, we define and study W¯α, the associated wave generator in the phase space of finite energy states. We prove the existence of the phase flow generated by W¯α, and describe its most relevant properties with a particular emphasis on the associated symplectic structure and scattering theory. © 2001 American Institute of Physics.
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    Quantum toroidal algebra Uq(sl2,tor) and R matrices (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2293-2308 
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    Notes: We show the existence of R matrices acting on the tensor product of a certain class of representations of the quantum toroidal algebra Uq(sl2,tor). In particular, the explicit expressions of R matrices acting on the tensor product of level 1 integrable highest weight representations of Uq(sl2&dbgcaret;) are obtained. Our approach is based on the work of Chari and Pressley. © 2001 American Institute of Physics.
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    Erratum: "Three flavor neutrino oscillations in matter" [J. Math. Phys. 41, 2768 (2000)] (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2345-2345 
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    The Hausdorff entropic moment problem (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2309-2314 
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    Notes: Our aim in this paper is twofold. First, to find the necessary and sufficient conditions to be satisfied by a given sequence of real numbers {ωn}n=0∞ to represent the "entropic moments" ∫[0,a][ρ(x)]ndx of an unknown non-negative, decreasing and differentiable (a.e.) density function ρ(x) with a finite interval support. These moments are called entropic moments because they are closely connected with various information entropies (Renyi, Tsallis, ...). Second, we outline an efficient method for the reconstruction of the density function from the knowledge of its first N entropic moments. © 2001 American Institute of Physics.
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    Chirality in the context of spin 〈fraction SHAPE="CASE"〉32 particles (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1599-1611 
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    Notes: In this paper we apply the chiral spinorial approach to the description of spin 〈fraction SHAPE="CASE"〉32 particles. Chiral components of rank 3 spinor fields are considered to be the dynamical variables of the theory. The free Lagrangian is built from the same principles as in the case of spin 1 and spin 2 particles: chiral symmetry at the free field level and chiral symmetry breakdown at the interaction level. We show how the chiral spinorial approach provides an unambiguous Lagrangian approach for massless spin 〈fraction SHAPE="CASE"〉32 particles. This approach provides a fairly rich set of effective Lagrangians for the interaction of spin 〈fraction SHAPE="CASE"〉32 particles. © 2001 American Institute of Physics.
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    High-frequency asymptotics for Maxwell's equations in anisotropic media Part II: Nonlinear propagation and frequency conversion (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1636-1654 
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    Notes: This paper is devoted to the derivation of the equations that govern the propagation and frequency conversion of pulses in noncentrosymmetric crystals. The method is based upon high-frequency expansions techniques for hyperbolic quasi-linear and semilinear equations. In the so-called geometric regime we recover the standard results on the frequency conversion of pulses in nonlinear crystals. In the diffractive regime we show that the anisotropy of the diffraction operator involves remarkable phenomena. In particular the phase matching angle of a divergent pulse depends on the distance between the waist and the crystal plate. Finally we detect a configuration where the beam propagation in a biaxial crystal involves the generation of spatial solitons thanks to an anomalous one-dimensional diffraction. © 2001 American Institute of Physics.
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    The braiding for representations of q-deformed affine sl2 (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 2156-2166 
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    Notes: We compute the braiding for the "principal gradation" of Uq(sl2&dbgcaret;) for |q|=1 from first principles, starting from the idea of a rigid braided tensor category. It is not necessary to assume either the crossing or the unitarity condition from S-matrix theory. We demonstrate the uniqueness of the normalization of the braiding under certain analyticity assumptions, and show that its convergence is critically dependent on the number theoretic properties of the number τ in the deformation parameter q=e2πiτ. We also examine the convergence using probability, assuming a uniform distribution for q on the unit circle. © 2001 American Institute of Physics.
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    Nonintegrability of Bianchi VIII Hamiltonian system (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1728-1743 
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    Notes: In this paper we study the Bianchi VIII cosmological dynamical system. Our aim is to show that this system is nonintegrable. To show this we use an extension of Ziglin theory made by Morales-Ruiz and Ramis. © 2001 American Institute of Physics.
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    Lie aspects of the dynamics of self-gravitating ellipsoids in n dimensions (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1761-1778 
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    Notes: In this paper we study the dynamics of self-gravitating ellipsoids in n dimensions, from the point of view of the Poisson structure of the dual of a suitable Lie algebra. When n=3 this was done by Rosenteel. In this setting we describe explicitly the ring of invariant functions. In the two-dimensional case we apply a technique due to Pedersen to find globally defined Darboux coordinates on the coadjoint orbits. Finally we derive a characterization of tensors coming from potentials, and use it to exhibit the dynamical equations of the ellipsoid in the Hamiltonian form. © 2001 American Institute of Physics.
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    Path integral for relativistic Aharonov–Bohm–Coulomb system on the pseudo-sphere (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1053-1065 
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    Notes: The Green's function for relativistic spinless Aharonov–Bohm–Coulomb (ABC) system on the pseudo-sphere Λ(2) is calculated using Kleinert's path integral representation for relativistic spinless particles. The energy spectrum and the corresponding wave functions are extracted for bound and scattering states. The results in the nonrelativistic and flat space limits are considered. © 2001 American Institute of Physics.
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    Nöther charges, Brown–York quasilocal energy, and related topics (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1173-1195 
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    Notes: The Lagrangian proposed by York et al. and the covariant first-order Lagrangian for general relativity are reviewed. They both deal with the (vacuum) gravitational field on a reference background and were conjectured to be equivalent. The two corresponding actions are compared and we show that the first one can in fact be obtained from the latter under suitable hypotheses. A conditioned correspondence among Nöther conserved quantities of covariant first-order Lagrangian, Brown–York quasilocal energy and the standard ADM Hamiltonian is also established. © 2001 American Institute of Physics.
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    On combined standard–nonstandard or hybrid (q,h)-deformations (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1236-1249 
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    Notes: Combined (q,h)-deformations proposed by Kupershmidt and Ballesteros–Herranz–Parashar are studied. In each case a transformation is shown to lead to an equivalent, standard q-deformation. We briefly indicate that appropriate singular limits of the same type of transformations can however lead from standard biparametric (p,q)-deformations to nonhybrid but biparametric nonstandard (g,h) ones. Finally a case of hybrid (q,h)-deformation is recalled, related to the superalgebra GL(1|1). © 2001 American Institute of Physics.
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    Differential geometry of GLh(1|1) (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1283-1295 
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    Notes: We construct a differential calculus on the quantum supergroup GLh(1|1) and obtain the h-deformed superalgebra of GLh(1|1). © 2001 American Institute of Physics.
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    Recursion operators of some equations of hydrodynamic type (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1309-1325 
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    Notes: We give a general method for constructing recursion operators for some equations of hydrodynamic type, admitting a nonstandard Lax representation. We give several examples for N=2 and N=3 containing the equations of shallow water waves and its generalizations with their first two general symmetries and their recursion operators. We also discuss a reduction of N+1 systems to N systems of some new equations of hydrodynamic type. © 2001 American Institute of Physics.
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    Quotient of a loop group and Witten genus (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1364-1383 
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    Notes: We define a Dirac–Ramond operator over the quotient (LG)/H of a loop group by a subgroup H of the compact Lie group G. We state the conjecture that its equivariant Index with respect of the natural circle action over the quotient of the loop group is equal to the Witten genus of the homogeneous manifold G/H. We motivate the conjecture by a short time argument which allows to come back to a Dirac–Ramond operator at the manner of Taubes on a limit model where all the computations can be done by hand. © 2001 American Institute of Physics.
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    To the Gel'fand–Tsetlin realization of irreducible representations of classical semisimple algebras (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1384-1396 
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    Notes: It is shown that the Gel'fand–Tsetlin realization of irreducible representations of the An algebra is directly connected with a linear exactly integrable system in the n-dimensional space. General solutions for this system is explicitly given. © 2001 American Institute of Physics.
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    Stability of nonconservative hyperbolic systems and relativistic dissipative fluids (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1426-1442 
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    Notes: A stability theorem for general quasi-linear symmetric hyperbolic systems (not necessarily conservation laws) is proved in this work. The key assumption is the "stability eigenvalue condition," which requires all the eigenvalues of the constant coefficient system symbol to have negative real part for nonzero Fourier frequency, decaying no faster than |ω|2 when |ω|→0. The decay of the solution to zero, as time grows to infinity, is proved when the space dimension is bigger than or equal to 3. As an application of the general theorem, stability is proved for the equations describing relativistic dissipative fluids. © 2001 American Institute of Physics.
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    Deformation of surfaces, integrable systems, and Chern–Simons theory (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1397-1417 
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    Notes: A few years ago, some of us devised a method to obtain integrable systems in (2+1)-dimensions from the classical non-Abelian pure Chern–Simons action via the reduction of the gauge connection in Hermitian symmetric spaces. In this article we show that the methods developed in studying classical non-Abelian pure Chern–Simons actions can be naturally implemented by means of a geometrical interpretation of such systems. The Chern–Simons equation of motion turns out to be related to time evolving two-dimensional surfaces in such a way that these deformations are both locally compatible with the Gauss–Mainardi–Codazzi equations and completely integrable. The properties of these relationships are investigated together with the most relevant consequences. Explicit examples of integrable surface deformations are displayed and discussed. © 2001 American Institute of Physics.
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    On the problem of algebraic completeness for the invariants of the Riemann tensor: I (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1474-1485 
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    Notes: We present a new determining set, CZ, of Riemann invariants which possesses the minimum degree property. From an analysis on the possible independence of CZ, we are led to the division of all space–times into two distinct, invariantly characterized, classes: a general class MG+, and a special, singular class MS. For each class, we provide an independent set of invariants (IG+⊂CZ and IS⊂CZ, respectively) which, with the results of a sequel paper, will be shown to be algebraically complete. © 2001 American Institute of Physics.
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    Ground state energy of massive scalar field inside a spherical region in the global monopole background (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 562-581 
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    Notes: Using the zeta function regularization method we calculate the ground state energy of scalar massive field inside a spherical region in the space–time of a pointlike global monopole. Two cases are investigated: (i) First, we calculate the Casimir energy inside a sphere of radius R and analyze the obtained result. We observe that this energy may be positive or negative depending on metric coefficient α and nonconformal coupling ξ. In the limit R→∞, this energy vanishes: (ii) In the second model, we surround the monopole by an additional sphere of radius r0〈R and consider the scalar field confined in the region between these two spheres. In this case, the ground state energy presents an additional contribution due to boundary at r0 which is divergent for small radius. Additional comments about renormalization are considered. © 2001 American Institute of Physics.
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    Symmetry properties and explicit solutions of the generalized Weierstrass system (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1250-1282 
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    Notes: The method of symmetry reduction is systematically applied to derive several classes of invariant solutions for the generalized Weierstrass system inducing constant mean curvature surfaces and to the associated two-dimensional nonlinear sigma model. A classification of subgroups with generic orbits of codimension one of the Lie point symmetry group for these systems provides a tool for introducing symmetry variables and reduces the initial systems to different nonequivalent systems of ordinary differential equations. We perform a singularity analysis for them in order to establish whether these ordinary differential equations have the Painlevé property. These ordinary differential equations can then be transformed to standard forms and next solved in terms of elementary and Jacobi elliptic functions. This results in a large number of new solutions and in some cases new interesting constant mean curvature surfaces are found. Furthermore, this symmetry analysis is extended to include conditional symmetries by subjecting the original system to certain differential constraints. In this case, several new types of nonsplitting algebraic, trigonometric, and hyperbolic multisoliton solutions have been obtained in explicit form. Some physical interpretation of these results in the areas of fluid membranes, string theory, two-dimensionl gravity, and cosmology are given. © 2001 American Institute of Physics.
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    Diagram projection rules for recoupling diagrams in the Racah–Wigner category (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1346-1363 
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    Notes: This paper gives three important techniques for recoupling coefficients of an arbitrary number or irreducible representations: factorization as a product of smaller degree recoupling coefficients, diagram projection projecting a recoupling diagram to obtain constraints on recoupling coefficients, and primitive expansion expressing a recoupling coefficient in terms of primitive recoupling coefficients. The first technique reduces a recoupling coefficient to its essential and simplest form. The second is many faceted allowing one to work at the recoupling level. Importantly, recoupling diagrams can be used to construct a complete set of constraints on the recoupling coefficients. The third allows large degree recoupling coefficients to be expressed in terms of primitive recoupling coefficients. An example of this is the fact that the 9j symbol is defined by the 3j and 6j symbols. © 2001 American Institute of Physics.
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    Harmonic functions and angular momentum for anyon systems (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1418-1425 
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    Notes: A method of construction of harmonic functions for the system of anyons on a plane is given. Spectra of angular momentum are derived. Anyonic statistics implies a restriction of the range of angular momentum which is stronger in comparison to the bosonic and fermion case. © 2001 American Institute of Physics.
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    Painlevé–Calogero correspondence revisited (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1443-1473 
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    Notes: We extend the work of Fuchs, Painlevé and Manin on a Calogero-like expression of the sixth Painlevé equation (the "Painlevé–Calogero correspondence") to the other five Painlevé equations. The Calogero side of the sixth Painlevé equation is known to be a nonautonomous version of the (rank one) elliptic model of Inozemtsev's extended Calogero systems. The fifth and fourth Painlevé equations correspond to the hyperbolic and rational models in Inozemtsev's classification. Those corresponding to the third, second and first are not included therein. We further extend the correspondence to the higher rank models, and obtain a "multi-component" version of the Painlevé equations. © 2001 American Institute of Physics.
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    Spherically symmetric solutions of the sixth order SU(N) Skyrme models (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5580-5595 
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    Notes: Following the construction described by Ioannidou et al. [J. Math. Phys. 40, 6353 (1999)], we use the rational map ansatz to construct analytically some topologically nontrivial solutions of the generalized SU(3) Skyrme model defined by adding a sixth order term to the usual Lagrangian. These solutions are radially symmetric and some of them can be interpreted as bound states of Skyrmions. The same ansatz is used to construct low-energy configuration of the SU(N) Skyrme model. © 2001 American Institute of Physics.
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    Investigation of the relativistic equivalent Hamiltonian in the LS coupling scheme (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5642-5651 
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    Notes: Armstrong's method of relativistic description of atoms in LS coupling using the equivalent operator is developed. Its form in terms of standard unit operators acting within a space of one shell is obtained. The interpretation of separate terms of equivalent Breit operator is investigated in a general case of nonequivalent electrons. The relativistic Dirac–Fock equations for the level and term in LS coupling are derived. The equivalent operator is applied to obtain the averages of relativistic operators too. © 2001 American Institute of Physics.
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    Asymptotics for the condensate multivortex solutions in the self-dual Chern–Simons CP(1) model (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5698-5712 
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    Notes: In this paper we study the asymptotics for the condensate multivortex solutions in the self-dual Chern–Simons CP(1) model. When the breaking parameter s belongs to (−〈fraction SHAPE="CASE"〉12,〈fraction SHAPE="CASE"〉12), we show that for any sequence of multivortex solutions which lies between suitable super- and subsolutions with respect to the Chern–Simons coupling constant κ, we can find a subsequence which converges to a constant depending only on s as κ goes to zero. Also we investigate the locally uniform convergence speed. © 2001 American Institute of Physics.
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    Three formulas for the off-diagonal density matrix of a dirac spinor, with an application (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 674-685 
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    Notes: Expressions for the off-diagonal density matrix of a Dirac spinor in space–time dimensions 2, 3, and 4 are derived. They are used to obtain formulas for the dual potential of a free Dirac current in two, three, and four dimensions of space–time. © 2001 American Institute of Physics.
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    Thermodynamics of trapped interacting bosons in one dimension (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 765-772 
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    Notes: On the basis of Bethe ansatz solution of bosons with δ-function interaction in a one-dimensional potential well, the thermodynamics equilibrium of the system in finite temperature is studied by using the strategy of Yang and Yang. The thermodynamics quantities, such as specific heat, etc., are obtained for the cases of the strong coupling and weak coupling limits respectively. © 2001 American Institute of Physics.
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    High order relativistic corrections to Keplerian motion (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 839-855 
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    Notes: The first terms of the general solution for an asymptotically flat stationary axisymmetric vacuum spacetime endowed with an equatorial symmetry plane are calculated from the corresponding Ernst potential up to seventh order in the radial pseudospherical coordinate. The metric is used to determine the influence of high order multipoles in the perihelion precession of an equatorial orbit and in the node line precession of a nonequatorial orbit with respect to a geodesic circle. Both results are written in terms of invariant quantities such as the Geroch–Hansen multipoles and the energy and angular momentum of the orbit. © 2001 American Institute of Physics.
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    Petrov type D Einstein space–times of embedding class two (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 863-875 
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    Notes: A space–time is of embedding class 2 if its curvature tensor can be written in terms of two symmetric tensors aαβ and bαβ which satisfy the Gauss, Codazzi, and Ricci equations. For an Einstein space–time the Ricci tensor is proportional to the metric tensor. Using the Petrov classification of the curvature tensor and canonical forms of aαβ and bαβ, this paper produces a list of the embedding class 2 Petrov type D Einstein space–times. After a summary of the basic equations and the previous work on embedding class 2 space–times, the field equations for Einstein space–times are expressed in a canonical form and the type D Petrov conditions applied. The resulting equations are solved and give two sets of metrics. The first are known metrics which are products of two 2-spaces of constant curvature and the second set is a generalization of the Kottler solution. The form of the second set of solutions depends upon whether the metric depends upon one or two of the four coordinates. © 2001 American Institute of Physics.
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    Batalin–Tyutin quantization of the spinning particle model (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5202-5211 
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    Notes: The spinning particle model for anyon is analyzed in the Batalin–Tyutin scheme of quantization in extended phase space. Here additional degrees of freedom are introduced in the phase space such that all the constraints in the theory are rendered first class, that is, commuting in the sense of Poisson brackets. Thus the theory can be studied without introducing the Dirac brackets which appear in the presence of noncommuting or second class constraints. In the present case the Dirac brackets make the configuration space of the anyon noncanonical and also, being dynamical variable dependent, poses problems for the quantization program. We show that previously obtained results (e.g., gyromagnetic ratio of anyon being 2) are recovered in the Batalin–Tyutin variable independent sector in the extended space. The Batalin–Tyutin variable contributions are significant and are computable in a straightforward manner. The latter can be understood as manifestations of the noncommutative space–time in the enlarged phase space. © 2001 American Institute of Physics.
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    Representations of the q-deformed algebra Uq′(so4) (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5389-5416 
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    Notes: We study the nonstandard q-deformation Uq′(so4) of the universal enveloping algebra U(so4) obtained by deforming the defining relations for skew-symmetric generators of U(so4). This algebra is used in quantum gravity and algebraic topology. We construct a homomorphism φ of Uq′(so4) to the certain nontrivial extension of the Drinfeld–Jimbo quantum algebra Uq(sl2)⊗2 and show that this homomorphism is an isomorphism. By using this homomorphism we construct irreducible finite-dimensional representations of the classical type and of the nonclassical type for the algebra Uq′(so4). It is proved that for q not a root of unity each irreducible finite-dimensional representation of Uq′(so4) is equivalent to one of these representations. We prove that every finite-dimensional representation of Uq′(so4) for q not a root of unity is completely reducible. It is shown how to construct (by using the homomorphism φ) tensor products of irreducible representations of Uq′(so4). [Note that no Hopf algebra structure is known for Uq′(so4).] These tensor products are decomposed into irreducible constituents. © 2001 American Institute of Physics.
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    Soliton solutions of XXZ lattice Landau–Lifshitz equation (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5457-5471 
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    Notes: Multisoliton solutions of the partially isotropic (classical) lattice Landau–Lifshitz equation are constructed. A trigonometric version of the dressing method is proposed to this aim. The dressing matrix is a matrix valued periodic function of the spectral parameter, and takes almost the same form as the L-matrix except for the number of poles. Both the easy-axis (J1=J2〈J3) and easy-plane (J1〈J2=J3) cases can be treated in a parallel way. © 2001 American Institute of Physics.
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    Erratum: "Hyperbolic Kac–Moody algebra from intersecting p-branes" [J. Math. Phys. 40, 4072 (1999)] (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5493-5493 
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    Notes: © 2001 American Institute of Physics.
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    Instantons in four-dimensional gauged O(5) Skyrme models (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4669-4683 
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    Notes: We consider a family of four-dimensional nonlinear sigma models based on an O(5) symmetric group, whose fields take their values on the 4-sphere S4. An SO(4)-subgroup of the model is gauged. The solutions of the model are characterized by two distinct topological charges, the Chern–Pontryagin charge of the gauge field and the degree of the map, i.e., the winding number, of the S4 field. The one-dimensional equations arising from the variation of the action density subjected to spherical symmetry are integrated numerically. Several properties of the solutions thus constructed are pointed out. The only solution with unit Chern–Pontryagin charge are the usual BPST instantons with zero S4 winding number, while solutions with unit S4 winding number have zero Chern–Pontryagin charge. © 2001 American Institute of Physics.
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    The disorder deviation in the deconfined phase (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4749-4756 
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    Topics: Mathematics , Physics
    Notes: A systematic study of the strongly interacting matter under extreme conditions via the form of the thermal ratio of the disorder deviation is presented. The evolution of Fermi and Bose particles (quarks and gluons) is studied in the framework of multi-particle correlation and distribution functions to predict the size of the finite-temperature deconfined phase. © 2001 American Institute of Physics.
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    Symmetries in the Hubbard model with n-fold orbital degeneracy (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4865-4872 
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    Notes: The present paper studies the symmetries of the Hubbard model of electrons with generally n-fold orbital degeneracy. It is shown that SUd(2n) and SUc(2n) symmetries hold, respectively, for the model with completely repulsive or attractive on-site interaction and that with partly attractive interactions. An extended Lieb–Mattis transformation is given to map these two symmetries into each other. The subsymmetry SUd(e)(n)⊗SUd(o)(n) is found to be shared by the two models with arbitrary chemical potential μ. By assuming at most two electrons on each site it is found that SUd(2n)P and SUc(2n)P both exist in each kind of the two models and consequently lead to a larger symmetry SUd(2n)P×SUc(2n)P. Another underlying symmetry (SUc(e)(2)P×(centered ellipsis)×SUc(e)(2)P)⊗(SUc(o)(2)P×(centered ellipsis)×SUc(o)(2)P) is also revealed for the unified U model under the excluding. The symmetry is valid for the partially attractive model with chemical potential μ=−U. © 2001 American Institute of Physics.
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    Graphical representation of the partition function of a one-dimensional δ-function Bose gas (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4883-4893 
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    Notes: The one-dimensional repulsive δ-function bose system is studied. By only using the Bethe ansatz equation, n-particle partition functions are exactly calculated. From this expression for the n-particle partition function, the n-particle cluster integral is derived. The results completely agree with those of the thermal Bethe ansatz (TBA). This directly proves the validity of the TBA. The theory of partitions and graphs is used to simplify the discussion. © 2001 American Institute of Physics.
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    Transformation formulas for double hypergeometric series related to 9-j coefficients and their basic analogs (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5417-5430 
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    Notes: In a recent paper, Ališauskas deduced different triple sum expressions for the 9-j coefficient of su(2) and suq(2). For a singly stretched 9-j coefficient, these reduce to different double sum series. Using these distinct series, we deduce a set of new transformation formulas for double hypergeometric series of Kampé de Fériet type and their basic analogs. These transformation formulas are valid for rather general parameters of the series, although a common feature is that all the series appearing here are terminating. It is also shown that the transformation formulas deduced here generate a group of transformation formulas, thus yielding an invariance group or symmetry group of particular double series. © 2001 American Institute of Physics.
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    Families of particular solutions to multidimensional partial differential equations (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5472-5492 
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    Notes: Dressing methods are known as productive tools for construction of the particular solutions to the big class of nonlinear partial differential equations (PDEs) which are integrable by the inverse scattering technique. Recently the modification of the dressing method based on the system of algebraic equations has been suggested which allows us to find the families of particular solutions to certain types of nonintegrable (in classical sense) nonlinear PDEs. This modification represents PDEs as closure reductions of an appropriate differential-difference system. In this article we study the dressing procedure in more detail. Particularly, we consider different families of particular solutions available through the dressing method based on the algebraic system. We give two examples of the differential-difference systems and related PDEs and point to other possible generalizations of the dressing method. © 2001 American Institute of Physics.
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    Algebraic treatment of super-integrable potentials (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4684-4706 
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    Notes: The so(2,1) Lie algebra is applied to three classes of two- and three-dimensional Smorodinsky–Winternitz super-integrable potentials for which the path integral discussion has been recently presented in the literature. We have constructed the Green's functions for two important super-integrable potentials in R2. Among the super-integrable potentials in R3, we have considered two examples, one is maximally super-integrable and another one minimally super-integrable. The discussion is made in various coordinate systems. The energy spectrum and the suitably normalized wave functions of bound and continuous states are then deduced. © 2001 American Institute of Physics.
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    Creation operators and Bethe vectors of the osp(1|2) Gaudin model (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4757-4778 
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    Notes: A Gaudin model based on the orthosymplectic Lie superalgebra osp(1|2) is studied. The eigenvectors of the osp(1|2) invariant Gaudin Hamiltonians are constructed by algebraic Bethe ansatz. Corresponding creation operators are defined by a recurrence relation. Furthermore, explicit solution to this recurrence relation is found. The action of the creation operators on the lowest spin vector yields Bethe vectors of the model. The relation between the Bethe vectors and solutions to the Knizhnik–Zamolodchikov equation of the corresponding super-conformal field theory is established. © 2001 American Institute of Physics.
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    n-symplectic algebra of observables in covariant Lagrangian field theory (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4827-4845 
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    Notes: n-symplectic geometry on the adapted frame bundle λ:LπE→E of an n=(m+k)-dimensional fiber bundle π:E→M is used to set up an algebra of observables for covariant Lagrangian field theories. Using the principle bundle ρ:LπE→J1π we lift a Lagrangian L:J1π→R to a Lagrangian L:=ρ*(L):LπE→R, and then use L to define a "modified n-symplectic potential" θ(circumflex)L on LπE, the Cartan–Hamilton–Poincaré (CHP) Rn-valued 1-form. If the lifted Lagrangian is nonzero, then (LπE,dθ(circumflex)L) is an n-symplectic manifold. To characterize the observables we define a lifted Legendre transformation φL from LπE into LE. The image QL:=φL(LπE) is a submanifold of LE, and (QL,d(θ(circumflex)|QL)) is shown to be an n-symplectic manifold. We prove the theorem that θ(circumflex)L=φL*(θ|QL), and pull back the reduced canonical n-symplectic geometry on QL to LπE to define the algebras of observables on the n-symplectic manifold (LπE,dθ(circumflex)L). To find the reduced n-symplectic algebra on QL we set up the equations of n-symplectic reduction, and apply the general theory to the model of a k-tuple of massless scalar fields on Minkowski space–time. The formalism set forth in this paper lays the ground work for a geometric quantization theory of fields. © 2001 American Institute of Physics.
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    Proof of a conjecture on the conductivity of checkerboards (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4873-4882 
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    Notes: In 1985 Mortola and Steffé conjectured a formula for the effective conductivity tensor of a checkerboard structure where the unit cell of periodicity is square and subdivided into four equal squares each having a different conductivity. In this article their conjecture is proven. The key idea is to superimpose suitably reflected potentials to obtain the solution to the dual problem. This is then related back to the original problem using a well known theorem of Keller, thereby proving the conjecture. The analysis also yields formulas relating the potentials in the four squares. Independently, Craster and Obnosov have obtained a completely different proof of the conjecture. © 2001 American Institute of Physics.
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    Calogero–Moser systems with periodic and doubly periodic interaction potentials and loop algebras (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4927-4937 
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    Notes: For a finite number of particles on the line pairwise interacting with 1/r2 potential, the positions are given by the eigenvalues of some time-dependent matrix. Infinite periodic or doubly periodic replication of the particles yields Calogero–Moser systems with periodic or doubly periodic interaction potential. We are thus led to consider matrices of infinite order, which are identified with Fourier series with matrix coefficients, depending on an additional parameter. These distributional loops of matrices (tori of matrices in the doubly periodic case) are shown to obey simple (partial) differential equations, which allow us to determine them explicitly. Thus we obtain the already known solution of the Calogero–Moser system on the circle, and provide a new insight for the system on the torus. © 2001 American Institute of Physics.
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    Expansion in the distance parameter for two vortices close together (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 182-191 
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    Notes: Static vortices close together are studied for two different models in two-dimensional Euclidean space. In a simple model for one complex field, an expansion in the parameters describing the relative position of two vortices can be given in terms of trigonometric and exponential functions. The results are then compared to those of the Ginzburg–Landau theory of a superconductor in a magnetic field at the point between type-I and type-II superconductivity. For the angular dependence a similar pattern emerges in both models. The differences for the radial functions are studied up to third order. © 2001 American Institute of Physics.
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    A single-mode quantum transport in serial-structure geometric scatterers (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4050-4078 
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    Notes: We study transport in quantum systems consisting of a finite array of N identical single-channel scatterers. A general expression of the S matrix in terms of the individual-element data obtained recently for potential scattering is rederived in this wider context. It shows in particular how the band spectrum of the infinite periodic system arises in the limit N→∞. We illustrate the result on two kinds of examples. The first are serial graphs obtained by chaining loops or T-junctions. Another example concerns geometric scatterers where the individual element consists of a surface with a pair of leads; we show that apart from the resonances coming from the decoupled-surface eigenvalues, such scatterers exhibit the high-energy behavior typical for the δ′ interaction for the physically interesting couplings. © 2001 American Institute of Physics.
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    Two- and three-dimensional Hamiltonians with shape invariance symmetry (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4122-4137 
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    Notes: Via a special dimensional reduction, that is, Fourier transforming over one of the coordinates of Casimir operator of su(2) Lie algebra and 4-oscillator Hamiltonian, we have obtained two- and three-dimensional Hamiltonian with shape invariance symmetry. Using this symmetry we have obtained their eigenspectrum. In the mean time we show equivalence of shape invariance symmetry and Lie algebraic symmetry of these Hamiltonians. © 2001 American Institute of Physics.
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    The Bargmann representation for the quantum mechanics on a sphere (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4138-4147 
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    Notes: The Bargmann representation is constructed corresponding to the coherent states for a particle on a sphere introduced in Kowalski and Rembielinski, J. Phys. A: 33, 6035 (2000). The connection is discussed between the introduced formalism and the standard approach based on the Hilbert space of square integrable functions on a sphere S2. © 2001 American Institute of Physics.
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    A robust approach to protein foldability measures based on spin-glass models (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4283-4290 
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    Notes: Spin-glass models and related methods have been applied to protein folding problems, often by assuming an underlying Gaussian distribution for the energy level distribution. In this paper, we derive robust foldability measures that relax the Gaussian distribution assumption implicit in current foldability and energy gap measures. © 2001 American Institute of Physics.
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    Translation-covariant Markovian master equation for a test particle in a quantum fluid (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4291-4312 
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    Notes: A recently proposed master equation in the Lindblad form is studied with respect to covariance properties and existence of a stationary solution. The master equation describes the interaction of a test particle with a quantum fluid, the so-called Rayleigh gas, and is characterized by the appearance of a two-point correlation function known as the dynamic structure factor, which reflects symmetry and statistical mechanics properties of the fluid. In the case of a free gas, all relevant physical parameters such as fugacity, ratio between the masses, momentum transfer, and energy transfer are put into evidence, giving an exact expansion of the dynamic structure factor. The limit in which these quantities are small is then considered. In particular, in the Brownian limit a Fokker–Planck equation is obtained in which the corrections due to quantum statistics can be explicitly evaluated and are given in terms of the Bose function g0(z) and the Fermi function f0(z). © 2001 American Institute of Physics.
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    A class of nonconservative Lagrangian systems on Riemannian manifolds (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4313-4326 
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    Notes: We generalize results of Rauch-Wojciechowski, Marciniak and Lundmark, concerning a class of nonconservative Lagrangian systems, from the Euclidean to the Riemannian case. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1388030
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    A family of completely integrable multi-Hamiltonian systems explicitly related to some celebrated equations (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4327-4344 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: By introducing a spectral problem with an arbitrary parameter, we derive a Kaup–Newell-type hierarchy of nonlinear evolution equations, which is explicitly related to many important equations such as the Kundu equation, the Kaup–Newell (KN) equation, the Chen–Lee–Liu (CLL) equation, the Gerdjikov–Ivanov (GI) equation, the Burgers equation, the modified Korteweg-deVries (MKdV) equation and the Sharma–Tasso–Olver equation. It is shown that the hierarchy is integrable in Liouville's sense and possesses multi-Hamiltonian structure. Under the Bargann constraint between the potentials and the eigenfunctions, the spectral problem is nonlinearized as a finite-dimensional completely integrable Hamiltonian system. The involutive representation of the solutions for the Kaup–Newell-type hierarchy is also presented. In addition, an N-fold Darboux transformation of the Kundu equation is constructed with the help of its Lax pairs and a reduction technique. According to the Darboux transformation, the solutions of the Kundu equation is reduced to solving a linear algebraic system and two first-order ordinary differential equations. It is found that the KN, CLL, and GI equations can be described by a Kundu-type derivative nonlinear Schrödinger equation involving a parameter. And then, we can construct the Hamiltonian formulations, Lax pairs and N-fold Darboux transformations for the Kundu, KN, CLL, and GI equations in explicit and unified ways. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1389288
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    Degenerate dynamical systems (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4383-4390 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Dynamical systems, whose symplectic structure degenerates, becoming noninvertible at some points along the orbits, are analyzed. It is shown that for systems with a finite number of degrees of freedom, like in classical mechanics, the degeneracy occurs on domain walls that divide phase space into nonoverlapping regions, each one describing a nondegenerate system, causally disconnected from each other. These surfaces are characterized by the sign of the Liouville flux density on them, behaving as sources or sinks of orbits. In this latter case, once the system reaches the domain wall, it acquires a new gauge invariance and one degree of freedom is dynamically frozen, while the remaining degrees of freedom evolve regularly thereafter. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1389088
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    Lorentzian regularization and the problem of point-like particles in general relativity (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4391-4418 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The two purposes of the article are (1) to present a regularization of the self-field of point-like particles, based on Hadamard's concept of "partie finie," that permits in principle to maintain the Lorentz covariance of a relativistic field theory, and (2) to use this regularization for defining a model of stress-energy tensor that describes point-particles in post-Newtonian expansions (e.g., 3PN) of general relativity. We consider specifically the case of a system of two point-particles. We first perform a Lorentz transformation of the system's variables which carries one of the particles to its rest frame, next implement the Hadamard regularization within that frame, and finally come back to the original variables with the help of the inverse Lorentz transformation. The Lorentzian regularization is defined in this way up to any order in the relativistic parameter 1/c2. Following a previous work of ours, we then construct the delta-pseudo-functions associated with this regularization. Using an action principle, we derive the stress-energy tensor, made of delta-pseudo-functions, of point-like particles. The equations of motion take the same form as the geodesic equations of test particles on a fixed background, but the role of the background is now played by the regularized metric. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1384864
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    Exactly calculable field components of electric dipoles in planar boundary (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 713-745 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Sommerfeld integrals for the electromagnetic fields in the planar boundary between air and a homogeneous, isotropic medium, due to a horizontal and a vertical electric dipole each lying along the interface, are examined in detail. In the case of the horizontal dipole, the tangential electric field is given in terms of series that involve confluent hypergeometric functions, namely, the Fresnel and exponential integrals. A similar exposition is presented for the magnetic and vertical electric fields of the vertical dipole. When the index of refraction of the adjacent space is of a sufficiently large magnitude, the derived series converge rapidly and uniformly with the distance from the source. Specifically, their rates of convergence are shown to be independent of distance. It is pointed out that the corresponding formulas of King et al. are valid down to any distance close to the source, where they smoothly connect to known "quasi-static" approximations. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1330731
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    On upper bounds for infinite Prandtl number convection with or without rotation (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 784-795 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Bounds for the bulk heat transport in Rayleigh–Benard convection for an infinite Prandtl number fluid are derived from the primitive equations. The enhancement of heat transport beyond the minimal conduction value (the Nusselt number Nu) is bounded in terms of the nondimensional temperature difference across the layer (the Rayleigh number Ra) according to Nu≤cRa2/5, where c〈1 is an absolute constant. This rigorous upper limit is uniform in the rotation rate when a Coriolis force, corresponding to the rotating convection problem, is included. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1336157
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    Acoustics of early universe—Lifshitz versus gauge-invariant theories (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 856-862 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Appealing to classical methods of order reduction, we reduce the Lifshitz system to a second order differential equation. We demonstrate its equivalence to well known gauge-invariant results. For a radiation dominated universe we express the metric and density corrections in their exact forms and discuss their acoustic character. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1335557
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    Relation between the solitons of Yang–Mills–Higgs fields in 2+1 dimensional Minkowski space–time and anti-de Sitter space–time (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4938-4946 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Yang–Mills–Higgs–Bogomolny equations in both 2+1 dimensional Minkowski space–time and 2+1 dimensional anti-de Sitter space–time are known to be integrable and their soliton solutions have already been obtained. In this article, we show that there is a natural relation between the Lax pairs and soliton solutions in these two space–times when the curvature changes from 0 to −1. The changes of the asymptotic behaviors of the solitons are also discussed. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1398585
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    The classification of plane symmetric spacetimes by isometries (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4947-4955 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A complete classification of plane symmetric Lorentzian manifolds according to their additional isometries and metrics (or classes of metrics) is obtained by solving the Killing equations. We obtain all metrics (or classes of metrics), that admit the group of motions Gr (where r=3,4,5,6,7 and 10) containing SO(2)(semidirect product)R2, the minimal symmetry inherited by the plane symmetric manifolds. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1385175
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    An algebraic approach to Macdonald–Koornwinder polynomials: Rodrigues-type formula and inner product identity (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 5020-5046 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study Macdonald–Koornwinder polynomials in the context of double affine Hecke algebras. Nonsymmetric Macdonald–Koornwinder polynomials are constructed by use of raising operators provided by a representation theory of the double affine Hecke algebra associated with A2l(2)-type affine root system. This enables us to evaluate diagonal terms of scalar products of the nonsymmetric polynomials algebraically. The Macdonald–Koornwinder polynomials are expressed by linear combinations of the nonsymmetric counterparts. We show a new proof of the inner product identity of the Macdonald–Koornwinder polynomials without Opdam–Cherednik's shift operators. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1398334
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    Euler number of instanton moduli space and Seiberg–Witten invariants (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 130-157 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show that a partition function of topological twisted N=4 Yang–Mills theory is given by Seiberg–Witten invariants on a Riemannian four manifolds under the condition that the sum of the Euler number and the signature of the four manifolds vanishes. The partition function is the sum of the Euler number of instanton moduli space when it is possible to apply the vanishing theorem. Also we obtain a relation of the Euler number labeled by the instanton number k with Seiberg–Witten invariants. All calculations in this article are done without assuming duality. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1331319
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    Fredholm indices and the phase diagram of quantum Hall systems (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 1-14 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quantized Hall conductance in a plateau is related to the index of a Fredholm operator. In this paper we describe the generic "phase diagram" of Fredholm indices associated with bounded and Toeplitz operators. We discuss the possible relevance of our results to the phase diagram of disordered integer quantum Hall systems. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1331317
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    Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 200-212 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Fokker–Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. However, there are both theoretical and empirical reasons to consider similar equations driven by strongly non-Gaussian noises. In particular, they yield strongly non-Gaussian anomalous diffusion which seems to be relevant in different domains of Physics. In this paper, we therefore derive a fractional Fokker–Planck equation for the probability distribution of particles whose motion is governed by a nonlinear Langevin-type equation, which is driven by a Lévy stable noise rather than a Gaussian. We obtain in fact a general result for a Markovian forcing. We also discuss the existence and uniqueness of the solution of the fractional Fokker–Planck equation. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1318734
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    Discontinuous trajectories of Lagrangian systems with singular hypersurface (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 309-329 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that a Lagrangian system whose Legendre transformation degenerates along a hypersurface behaves in a strange manner by jumping from time to time without any "visible cause." In such a jump the system changes instantaneously its coordinates as well as its momenta. Necessary elements of the general theory of such systems are reported and a detailed description of a postrelativistic oscillator showing such a behavior is given. © 2001 American Institute of Physics.
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    Unimodular relativity and cosmological constant (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 340-346 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Unimodular relativity is a theory of gravity and space–time with a fixed absolute space–time volume element, the modulus, which we suppose is proportional to the number of microscopic modules in that volume element. In general relativity an arbitrary fixed measure can be imposed as a gauge condition, while in unimodular relativity it is determined by the events in the volume. Since this seems to break general covariance, some have suggested that it permits a nonzero covariant divergence of the material stress-energy tensor and a variable cosmological "constant." In Lagrangian unimodular relativity, however, even with higher derivatives of the gravitational field in the dynamics, the usual covariant continuity holds and the cosmological constant is still a constant of integration of the gravitational field equations. © 2001 American Institute of Physics.
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    The complex Bateman equation in a space of arbitrary dimension (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 453-462 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The general solution to the complex Bateman equation in a space of arbitrary dimensions is constructed. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1286230
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    On the classification of irreducible finite-dimensional representations of Uq′(so3) algebra (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 472-500 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In an earlier work [M. Havlícek et al., J. Math. Phys. 40, 2135 (1999)] we defined for any finite dimension five nonequivalent irreducible representations of the nonstandard deformation Uq′(so3) of the Lie algebra so3 where q is not a root of unity [for each dimension only one of them (called classical) admits limit q→1]. In the first part of this paper we show that any finite-dimensional irreducible representation is equivalent to some of these representations. In the case qn=1 we derive new Casimir elements of Uq′(so3) and show that a dimension of any irreducible representation is not higher than n. These elements are Casimir elements of Uq′(som) for all m and even of Uq′(isom+1) due to Inönu–Wigner contraction. According to the spectrum of one of the generators, the representations are found to belong to two main disjoint sets. We give full classification and explicit formulas for all representations from the first set (we call them nonsingular representations). If n is odd, we have full classification also for the remaining singular case with the exception of a finite number of representations. © 2001 American Institute of Physics.
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    Capacity of quantum channels using product measurements (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 87-98 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The capacity of a quantum channel for transmission of classical information depends in principle on whether product states or entangled states are used at the input, and whether product or entangled measurements are used at the output. We show that when product measurements are used, the capacity of the channel is achieved with product input states, so that entangled inputs do not increase capacity. We show that this result continues to hold if sequential measurements are allowed, whereby the choice of successive measurements may depend on the results of previous measurements. We also present a new simplified expression which gives an upper bound for the Shannon capacity of a channel, and which bears a striking resemblance to the well-known Holevo bound. © 2001 American Institute of Physics.
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    Water at supercritical conditions: A first principles study (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 2219-2227 
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    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We analyze, via first principles molecular dynamics, the structural and electronic properties of water close to and above the critical point. Contrary to the ordinary liquid state, at supercritical conditions the hydrogen bond network is destabilized to various extents and the continuous breaking and reformation of hydrogen bonded structures allow large density and dipole fluctuations that, in turn, can significantly affect the dielectric properties of the solvent. Close to the critical point, where the density is very low, small clusters, mainly dimers and trimers, are the dominant features, but many molecules exhibit no H-bond. On the other hand, at higher densities, more extended structures appear, but still a continuous network cannot form. In both cases, H-bond configurations that are anomalous with respect to the normal liquid phase appear. These features strongly affect the solvent properties of supercritical water with respect to those of ambient water. They most likely vary continuously as a function of temperature, pressure and density and, hence, can be tuned to optimize the desired chemical process. © 2001 American Institute of Physics.
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    Analysis of solvation structure and thermodynamics of ethane and propane in water by reference interaction site model theory using all-atom models (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 2228-2236 
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    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Following our previous paper on methane [Cui and Smith, J. Chem. Phys. 113, 10240 (2000)], we study the solvation structures and thermodynamics of ethane and propane in water at the infinite dilution limit by using the hypernetted chain closure reference interaction site model (HNC-RISM) theory with all-atom representations for solute molecules. At four thermodynamic states: temperature T=283.15, 298.15, 313.15, 328.15 K and the corresponding bulk water density ρ=0.9997, 0.9970, 0.9922, 0.9875 g cm−3, all the atomic solute–solvent radial distribution functions are obtained, and the corresponding running coordination numbers and the hydration free energies, energies, enthalpies, and entropies are calculated with the radial distribution functions as input. The hydration structures of ethane and propane are presented and analyzed at the atomic level in terms of the atomic solute–solvent radial distribution functions. With the optimized nonbonded potential parameters based on the CHARMM96 all-atom model for alkanes [Yin and Mackerell, J. Comput. Chem. 19, 334 (1998)], the ethane and propane hydration thermodynamic properties predicted by the HNC-RISM theory are improved in the specified temperature range (10–55 °C). © 2001 American Institute of Physics.
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    Combined fluctuating charge and polarizable dipole models: Application to a five-site water potential function (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 2237-2251 
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    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a general formalism for polarizable electrostatics based on fluctuating bond-charge increments and polarizable dipoles and its application to a five-site model for water. The parametrization is based largely on quantum-chemical calculations and should be easily transferable to other molecules. To examine basis-set effects we parametrized two models from two sets of quantum calculations, using the aug-cc-pVTZ and aug-cc-pVQZ basis sets. We computed several gas-phase and condensed-phase properties and compared with experiment or ab initio calculations as available. The models are quite similar and give condensed-phase properties at ambient conditions that are in reasonable accord with experiment, but evince errors consistent with a liquid-state dipole moment that is slightly too large. The model fit to the aug-cc-pVTZ basis set has a smaller liquid-phase dipole moment and thus gives a somewhat better description of liquid water at ambient conditions. This model also performs well away from room temperature, deviating less than 2% from the experimental density from 0 to 100 °C, and showing good agreement with experimental radial distribution functions, although the temperature of maximum density (∼20 °C) is slightly too high and the model somewhat underpredicts the persistence of the hydrogen-bond network at elevated temperatures. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1376165
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    A general nuclear magnetic resonance analysis of hetero-association of aromatic molecules in aqueous solution (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 2252-2266 
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    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A general nuclear magnetic resonance analysis of a statistical-thermodynamical model of hetero-association of aromatic molecules in solution has been developed to take "edge effects" into consideration, i.e., the dependence of proton chemical shifts on the position of the molecule situated inside or at the edge of the aggregate. This generalized approach is compared with a previously published model, where an average contribution to proton shielding is considered irrespective of the position of the molecule in the stack. Association parameters have been determined from experimental concentration and temperature dependences of 500 MHz proton chemical shifts of the hetero-association of the acridine dye, proflavine, and the phenanthridinium dye, ethidium bromide, in aqueous solution. Differences in the parameters in the range 10%–30% calculated using the basic and generalized approaches have been found to depend substantially on the magnitude of the equilibrium hetero-association constant Khet—the larger the value of Khet, the higher the discrepancy between the two methods. © 2001 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.1359767
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