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  • 1
    Electronic Resource
    Electronic Resource
    On a theorem of Weyl (1984)
    Springer
    Integral equations and operator theory 7 (1984), S. 431-435 
    Details
    ISSN: 1420-8989
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a short proof of the theorem of Weyl, as generalized by von Neumann, that for any hermitian operator there exists a Hilbert-Schmidt perturbation of arbitrarily small Hilbert-Schmidt norm such that the sum has purely point spectrum. The proof consists of a simple construction of the perturbation. *** DIRECT SUPPORT *** A6515003 00004
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01208383
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  • 2
    Electronic Resource
    Electronic Resource
    Errata (1985)
    Springer
    Integral equations and operator theory 8 (1985), S. 892-894 
    Details
    ISSN: 1420-8989
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01213798
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  • 3
    Electronic Resource
    Electronic Resource
    Condensation in a variational problem on the space of measures (1992)
    Springer
    Archive for rational mechanics and analysis 118 (1992), S. 245-256 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study a variational problem on the space of bounded measures. The problem arises in a model of an interacting Bose gas. By reducing the Euler-Lagrange equations to a second-order non-linear differential equation we give a full description of the minimizing measure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00387897
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  • 4
    Electronic Resource
    Electronic Resource
    Dilations of dynamical semi-groups (1976)
    Springer
    Communications in mathematical physics 50 (1976), S. 219-227 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We prove the existence of isometric and unitary dilations of a class of semi-groups of completely positive maps on an algebra of operators on a Hilbert space. The result has relevance to the problem of embedding an open quantum mechanical system in a closed one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609402
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  • 5
    Electronic Resource
    Electronic Resource
    The equilibrium states of the free Boson gas (1974)
    Springer
    Communications in mathematical physics 36 (1974), S. 1-18 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The generating functional of the cyclic representation of the canonical commutation relations for the equilibrium state of the free Boson gas is calculated, using a method due to Kac, as the thermodynamic limit of the grand canonical generating functional. The relation to the work of Araki and Woods is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01646022
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  • 6
    Electronic Resource
    Electronic Resource
    Symmetric states of composite systems (1988)
    Springer
    Letters in mathematical physics 15 (1988), S. 255-260 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Størmer proved a theorem on the integral decomposition of symmetric states on a C *-algebra % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0dd9Lq-Jdr% pepu0dd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxc9qr0-vr% 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaaxacabaGaey% 4LIqmaleqabaGaey4fIOcaaaaa!387C!v\mathop\otimes \limits^ *$$ ℬ. Motivated by problems in statistical mechanics, we define summetric states on a composite algebra A ⊗ ( % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0dd9Lq-Jdr% pepu0dd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxc9qr0-vr% 0-vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaamaaxacabaGaey% 4LIqmaleqabaGaey4fIOcaaaaa!387C!v\mathop\otimes \limits^ *$$ ℬ)and extend Størmer's theorem to this situation. Applications to spin-boson models are sketched.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398595
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  • 7
    Electronic Resource
    Electronic Resource
    Independent oscillator model of a heat bath: Exact diagonalization of the Hamiltonian (1988)
    Springer
    Journal of statistical physics 53 (1988), S. 439-455 
    Details
    ISSN: 1572-9613
    Keywords: Coupled oscillators ; heat bath ; free energy ; quantum dissipation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The problem of a quantum oscillator coupled to an independent-oscillator model of a heat bath is discussed. The transformation to normal coordinates is explicitly constructed using the method of Ullersma. With this transformation an alternative derivation of an exact formula for the oscillator free energy is constructed. The various contributions to the oscillator energy are calculated, with the aim of further understanding this formula. Finally, the limitations of linear coupling models, such as that used by Ullersma, are discussed in the form of some critical remarks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011565
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  • 8
    Electronic Resource
    Electronic Resource
    The equilibrium thermodynamics of a spin-boson model (1988)
    Springer
    Journal of statistical physics 50 (1988), S. 1201-1220 
    Details
    ISSN: 1572-9613
    Keywords: Spins coupled to a boson field ; Dicke maser model ; second-order phase transition ; large deviations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider the equilibrium thermodynamics of a Dicke-type model forN identical spins of arbitrary magnitude interacting linearly and homogeneously with a boson field in a volumeV N, in the limitN→∞,V N→∞, withN/V N=const. The system exhibits a second-order phase transition; complete information on the spin polarizations and their correlations is obtained. The proofs use a general result on the free energy of quantum spin systems based on the large deviation principle and the Berezin-Lieb inequalities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01019161
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  • 9
    Electronic Resource
    Electronic Resource
    The large deviation principle and some models of an interacting boson gas (1988)
    Springer
    Communications in mathematical physics 118 (1988), S. 61-85 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This is a study of the equilibrium thermodynamics of the Huang-Yang-Luttinger model of a boson gas with a hard-sphere repulsion using large deviation methods; we contrast its properties with those of the mean field model. We prove the existence of the grand canonical pressure in the thermodynamic limit and derive two alternative expressions for the pressure as a function of the chemical potential. We prove the existence of condensate for values of the chemical potential above a critical value and verify a prediction of Thouless that there is a jump in the density of condensate at the critical value. We show also that, at fixed mean density, the density of condensate is an increasing function of the strength of the repulsive interaction. In an appendix, we give proofs of the large deviation results used in the body of the paper.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01218477
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  • 10
    Electronic Resource
    Electronic Resource
    The Yang-Yang thermodynamic formalism and Large Deviations (1989)
    Springer
    Communications in mathematical physics 124 (1989), S. 365-402 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The partition function for a one-dimensional system of Bosons with repulsive delta-function interaction is investigated. We prove that if the Bethe Ansatz eigenfunctions form a complete set then the grand canonical pressure is given by the Yang-Yang formula. The proof uses a probabilistic formalism to express the partition function as an expectation with respect to a probability measure on a Banach space of measures; the asymptotic behaviour of the expectation in the thermodynamic limit is determined by the Large Deviation Principle. This method is applicable in situations in which the Hamiltonian can be diagonalised using the Bethe Ansatz.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01219656
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