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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 5598-5626 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We base a treatment of the dissipative, multi-mode version of Dicke laser model on the theory of completely positive dynamical semigroups and quantum Markov processes. This leads to new results at both the mathematical and physical levels. On the physical side, it provides a generalization of the Hepp–Lieb model that admits both chaotic and polychromatic laser radiation. On the mathematical side, it extends the theory of dynamical semigroups to a regime where the generators are perturbed by unbounded derivations. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 2730-2747 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In a recent article, Alli and Sewell [J. Math. Phys. 36, 5598 (1995)] formulated a new version of the Dicke–Hepp–Lieb laser model in terms of quantum dynamical semigroups, and thereby extended the macroscopic picture of the model. In the present article, we complement that picture with a corresponding microscopic one, which carries the following new results. (a) The local microscopic dynamics of the model is piloted by the classical, macroscopic field, generated by the collective action of its components; (b) the global state of the system carries no correlations between its constituent atoms after transient effects have died out; and (c) in the latter situation, the state of the system at any time t maximizes its entropy density, subject to the constraints imposed by the instantaneous values of its macroscopic variables. © 1998 American Institute of Physics.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 2324-2334 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We derive macroscopic electrohydrodynamical equations of Euler and Maxwell from the many-particle Schrödinger equation of the Jellium model, subject to viable initial conditions, together with certain simple assumptions of macroscopic regularity. The dynamics of the model becomes tractable, on a suitable macroscopic scale and in the limit where its size becomes infinite, because of simple scaling properties and the long range of the Coulomb forces. Our derivation of its phenomenological dynamics is obtained via that of the classical Vlasov equation.
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 2053-2071 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We present a general, model-independent, quantum statistical derivation of superconductive electrodynamics from the assumptions of off-diagonal long range order (ODLRO), local gauge covariance, and thermodynamic stability. On this basis, we obtain the Meissner and Josephson effects, the quantization of trapped magnetic flux, and the metastability of supercurrents. A key to these results is that the macroscopic wave function, specified by the ODLRO condition, enjoys the rigidity property that London [Superfluids, Vol. 1 (Wiley, London, 1950)], envisaged for the microstate of a superconductor. © 1997 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 55 (1977), S. 63-66 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We extend the characterisation of metastability, as given in [1] for classical systems, to show that quantal lattice systems with suitable long range forces can support metastable states.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 71 (1980), S. 1-28 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We formulate the equilibrium correlation functions for local observables of an assembly of non-relativistic, neutral gravitating fermions in the limit where the number of particles becomes infinite, and in a scaling where the region θ, to which they are confined, remains fixed. We show that these correlation functions correspond, in the limit concerned, to states on the discrete tensor product $$\mathop \otimes \limits_{x \in \Omega } A_x $$ , where the $$A_x 's$$ are copies of the gauge invariantC*-algebra $$A$$ of the CAR overL 2(R 3). The equilibrium states themselves are then given by $$\mathop \otimes \limits_{x \in \Omega } \bar \omega _{\varrho 0(x)} $$ , where $$\bar \omega _\varrho $$ , is the Gibbs state on $$A$$ for an infinitely extended ideal Fermi gas at density ϱ, and where ϱ0 is the normalised density function that minimises the Thomas-Fermi functional, obtained in [2], governing the equilibrium thermodynamics of the system.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 52 (1977), S. 103-109 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We formulate local thermodynamical stability conditions for states of quantum lattice systems, and show that these conditions are implied by, and in the case of translationally invariant states equivalent to, those of Kubo-Martin-Schwinger (KMS).
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 55 (1977), S. 53-61 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We prove that local thermodynamical stability (LTS), as defined in [1], implies the KMS conditions in quantum lattice systems, without any assumption of translational invariance. This result, together with those of [1], establishes the equivalence between the LTS and the KMS conditions for such systems.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 79 (1981), S. 9-24 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We derive the Vlasov hydrodynamics from the microscopic equations of a quantum mechanical model, which simulates that of an assembly of gravitating particles. In addition we show that the local microscopic dynamics of the model corresponds, on a suitable time-scale, to that of an ideal Fermi gas.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 22 (1991), S. 239-250 
    ISSN: 1573-0530
    Keywords: 81T13 ; 82D55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We provide an axiomatic Euclidean field-theoretic treatment of the Meissner and Abelian Higgs effects, which extends our previous method to a fully quantum theoretic model of a gauge field, with U(1) symmetry, coupled to a scalar field. Our main results are that the former effect implies the latter one, and ensues from the condition of off-diagonal long-range order.
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