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  • Articles  (150,175)
  • 1995-1999  (136,312)
  • 1950-1954  (13,863)
  • Mathematics  (91,229)
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  • Articles  (150,175)
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  • 1
    Electronic Resource
    Electronic Resource
    Nonextensive Bose–Einstein condensation model (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1268-1279 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The imperfect Boson gas supplemented with a gentle repulsive interaction is completely solved. In particular, it is proved that it has nonextensive Bose–Einstein condensation, i.e., there is condensation without macroscopic occupation of the ground (k=0) state level. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532800
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  • 2
    Electronic Resource
    Electronic Resource
    Dynamical semigroups for interacting quantum and classical systems (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1300-1316 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A mathematical framework for the completely positive semigroup coupling between classical and quantum systems is proposed. The coupling ensures a flow of information from the quantum system to the classical one and the influence of the classics on the dynamics of the quantum system in a dissipative way. The classical evolution on average is modified by the expectation value of some quantum operator. Examples of a classical particle moving along a geodesic line in a curved space interacting with the quantum system, and the coupling of a two state quantum system to all pure states, are discussed. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532803
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  • 3
    Electronic Resource
    Electronic Resource
    Toward quantum mathematics. I. From quantum set theory to universal quantum mechanics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1344-1358 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We develop the old idea of von Neumann of a set theory with an internal quantum logic in a modern categorical guise [i.e., taking the objects of the category H of (pre-)Hilbert spaces and linear maps as the sets of the basic level]. We will see that in this way it is possible to clarify the relationship between categorification and quantization and besides this to understand that in some sense a categorificational approach to quantization is a discretized version of the one taken by noncommutative geometry. The tower of higher categorifications will appear as the analog of the von Neumann hierarchy of classical set theory (where by classical set theory, we will understand the usual Zermelo–Fraenkel system). Finally, we make a suggestion of how to understand all the different categorifications as different realizations of one and the same abstract structure by viewing quantum mechanics as universal in the sense of category theory. This gives the possibility to view extended topological quantum field theories purely as involving an abstract notion of quantum mechanics plus representation theory without the need to enlarge the class of kinematic structures of quantum systems on each step of categorification. In a future part of the work we will apply the language developed here to deal especially with the question of a categorification of the manifold notion. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532806
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  • 4
    Electronic Resource
    Electronic Resource
    Extended Jordanian twists for Lie algebras (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4569-4586 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebra B∨ of sl(N) the explicit expressions are obtained for the twist element F, universal R-matrix and the corresponding canonical element T. It is shown that the twisted Hopf algebra UF(B∨) is self-dual. The cohomological properties of the involved Lie bialgebras are studied to justify the existence of a contraction from the Dinfeld–Jimbo quantization to the Jordanian one. The construction of the twist is generalized to a certain type of inhomogenious Lie algebras. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532987
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  • 5
    Electronic Resource
    Electronic Resource
    Operator representations of a q-deformed Heisenberg algebra (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4596-4605 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A class of well-behaved * -representations of a q-deformed Heisenberg algebra previously introduced [Phys. Lett. B 291, 273 (1992); Z. Phys. C 64, 335 (1994)] is studied and classified. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532989
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  • 6
    Electronic Resource
    Electronic Resource
    On the root mean square quantitative chirality and quantitative symmetry measures (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4587-4595 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The properties of the root mean square chiral index of a d-dimensional set of n points, previously investigated for planar sets, are examined for spatial sets. The properties of the root mean squares direct symmetry index, defined as the normalized minimized sum of the n squared distances between the vertices of the d-set and the permuted d-set, are compared to the properties of the chiral index. Some most dissymetric figures are analytically computed. They differ from the most chiral figures, but the most dissymetric 3-tuples and the most chiral 3-tuples have a common remarkable geometric property: the squared lengths of the sides are each equal to three times a squared distance vertex to the mean point. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532988
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  • 7
    Electronic Resource
    Electronic Resource
    Asymptotics of the scattering coefficients for a generalized Schrödinger equation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3701-3709 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The generalized Schrödinger equation d2ψ/dx2+F(k)ψ=[ikP(x)+Q(x)]ψ is considered, where P and Q are integrable potentials with finite first moments and F satisfies certain conditions. The behavior of the scattering coefficients near zeros of F is analyzed. It is shown that in the so-called exceptional case, the values of the scattering coefficients at a zero of F may be affected by P(x). The location of the k-values in the complex plane where the exceptional case can occur is studied. Some examples are provided to illustrate the theory. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532920
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  • 8
    Electronic Resource
    Electronic Resource
    On the dynamics of the Holstein model from the anticontinuous limit (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3710-3717 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider the Holstein model describing an electron interacting with a lattice of identical oscillators. We remark that the on site system (i.e., the system in which the interaction between the different sites of the lattice vanishes) is integrable and anisocronous. This allows us to apply some recent Nekhoroshev-type results to show that corresponding to the majority of initial data in which the electron probability is concentrated on a finite number of sites, the electron probability distribution is approximatively constant for times growing exponentially with the inverse of the coupling parameter. Moreover, for the same times, the total energy of the oscillator system is approximatively constant. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532921
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  • 9
    Electronic Resource
    Electronic Resource
    Generalized Lamé functions. I. The elliptic case (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1595-1626 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We present and study a class of functions associated with the two-particle quantum relativistic Calogero–Moser system with elliptic interactions. The functions may be viewed as joint eigenfunctions of two independent commuting analytic difference operators, one of which is the defining quantum dynamics; The second one is obtained by interchanging the step size and the imaginary period. The functions depend on parameters that are dense in the natural parameter domain. In essence, they consist of products of Weierstrass σ-functions and plane waves. The zeros of the σ-functions satisfy a constraint system encoding both Schrödinger equations at once. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532822
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  • 10
    Electronic Resource
    Electronic Resource
    A reverse log-Sobolev inequality in the Segal-Bargmann space (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1677-1695 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This article is based on recent results of the author on the properties of the reproducing kernel of the Segal-Bargmann space. Those results are used here to demonstrate a family of energy-entropy inequalities in the Segal-Bargmann space. In some cases this is a log-Sobolev inequality while in other cases this is actually a reverse log-Sobolev inequality, which means that the energy term is bounded above by the entropy term, plus a norm term. This implies that in the Segal-Bargmann space the entropy is finite if and only if the energy is finite. Applications of this result to the Segal-Bargmann transform are given as well as a discussion of its possible relation with reverse hypercontractivity. It should be noted that all of the results of this article are proved without using hypercontractivity estimates. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532825
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