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  • 1
    Electronic Resource
    Electronic Resource
    Infinite degeneracy for a Landau Hamiltonian with Poisson impurities (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6304-6314 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider a single-band approximation to the random Schrödinger operator in an external magnetic field. The random potential consists of delta functions of random strengths whose positions have a Poisson distribution. We prove that if the magnetic field is sufficiently high compared to the density of scatterers, then with probability one there exists an infinitely degenerate eigenenergy coinciding with the first Landau level in the absence of a random potential. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532214
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  • 2
    Electronic Resource
    Electronic Resource
    The spectrum of a magnetic Schrödinger operator with randomly located delta impurities (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 2805-2825 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider a single band approximation to the random Schrödinger operator in an external magnetic field. The spectrum of such an operator has been characterized in the case where delta impurities are located on the sites of a lattice. In this paper we generalize these results by letting the delta impurities have random positions as well as strengths; they are located in squares of a lattice with a general bounded distribution. We characterize the entire spectrum of this operator when the magnetic field is sufficiently high. We show that the whole spectrum is pure point, the energy coinciding with the first Landau level is infinitely degenerate, and that the eigenfunctions corresponding to other Landau band energies are exponentially localized. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533272
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  • 3
    Electronic Resource
    Electronic Resource
    Localization in single Landau bands (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 1574-1595 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider a single-band approximation to the random Schrödinger operator in an external magnetic field. The random potential is taken to be constant on unit squares and i.i.d. on each square with a bounded distribution. We prove that the eigenstates corresponding to energies at the edges of the Landau band are localized. This is an important ingredient in the theory of the Quantum Hall Effect. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531469
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  • 4
    Electronic Resource
    Electronic Resource
    Large deviations in a semi-infinite layered ferromagnet with mean-field interactions: Classical and quantum models (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 4774-4784 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider the probability distribution in a classical semi-infinite layered ferromagnet with mean-field interactions and prove that this satisfies a large deviation principle, giving the rate function explicitly. For an analogous quantum system we show that the limiting states are product states, which are completely characterized by the classical mean-field solutions. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530919
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  • 5
    Electronic Resource
    Electronic Resource
    Diamagnetic currents (1988)
    Springer
    Communications in mathematical physics 117 (1988), S. 215-241 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the diamagnetic surface currents of particles in thermal equilibrium submitted to a constant magnetic field. The current density of independent electrons with Boltzmann (respectively Fermi) statistics has a gaussian (respectively exponential) bound for its fall off into the bulk. For a system of interacting particles at low activity with Boltzmann statistics, the current density is localized near to the boundary and integrable when the two-body potential decays as |x|−α, α 〉4, α〉4, in three dimensions. In all cases, the integral of the current density is independent of the nature of the confining wall and correctly related to the bulk magnetisation. The results hold for hard and soft walls and all field strength. The analysis relies on the Feynman-Kac-Ito representation of the Gibbs state and on specific properties of the Brownian bridge process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01223591
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  • 6
    Electronic Resource
    Electronic Resource
    The free boson gas in a rotating bucket (1975)
    Springer
    Communications in mathematical physics 45 (1975), S. 115-131 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01629242
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    A perturbed mean field model of an interacting boson gas and the large deviation principle (1990)
    Springer
    Communications in mathematical physics 127 (1990), S. 41-69 
    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 a mean-field model of an interacting boson gas perturbed by a term quadratic in the occupation numbers of the free-gas energy-levels. We prove the existence of the pressure in the thermodynamic limit. We obtain also a variational formula for the pressure; this enables us to compare the effect of a smooth quadratic perturbation with that of a singular one (the Huang-Yang-Luttinger model). The proof uses a large deviation result for the occupation measure of the free boson gas which is of independent interest.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096493
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  • 9
    Electronic Resource
    Electronic Resource
    The pressure in the Huang-Yang-Luttinger model of an interacting boson gas (1990)
    Springer
    Communications in mathematical physics 128 (1990), S. 231-245 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This completes our study of the equilibrium thermodynamics of the Huang-Yang-Luttinger model of a boson gas with a hard-sphere repulsion. In an earlier paper we obtained a lower bound on the pressure, but our proof of an upper bound held only for a truncated version of the model. In this paper we establish an upper bound on the pressure in the full model; the upper and lower bounds coincide and provide a variational formula for the pressure. The proof relies on recent second-level large deviation results for the occupation measure of the free boson gas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02108780
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  • 10
    Electronic Resource
    Electronic Resource
    The full diagonal model of a Bose gas (1993)
    Springer
    Communications in mathematical physics 156 (1993), S. 37-65 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper is the final one in a series in which we investigate some models of an interacting Bose gas using Varadhan's large deviation version of Laplacian asymptotics; in it we study the equilibrium thermodynamics of the full diagonal model of a Bose gas. We obtain a formula expressing the pressure, in the thermodynamic limit, as the supremum of a functional over the space of positive bounded measures. We analyse this formula for a large class of interaction kernels and show that there is a critical temperature below which there is Bose-Einstein condensation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096732
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