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  • Articles  (231)
Collection
  • Articles  (231)
Journal
  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 891-898 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general class of hopping models on a finite bipartite lattice is considered, including the Hubbard model and the Falicov–Kimball model. For the half-filled band, the single-particle density matrix ρ(x,y) in the ground state and in the canonical and grand canonical ensembles is shown to be constant on the diagonal x=y, and to vanish if x≠y and if x and y are on the same sublattice. For free electron hopping models, it is shown in addition that there are no correlations between sites of the same sublattice in any higher order density matrix. Physical implications are discussed.
    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 31 (1990), S. 594-599 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An upper bound is proved for the Lp norm of Woodward's ambiguity function in radar signal analysis and of the Wigner distribution in quantum mechanics when p〉2. A lower bound is proved for 1≤p〈2. In addition, a lower bound is proved for the entropy. These bounds set limits to the sharpness of the peaking of the ambiguity function or Wigner distribution. The bounds are best possible and equality is achieved in the Lp bounds if and only if the functions f and g that enter the definition are both Gaussians.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 172 (1971), S. 0 
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Notes: The Hubbard Hamiltonian, while not one of the most successful models for π electrons in benzene, has been extensively investigated in the literature. As part of our general study of that model, we have computed all the energy levels for all values of the repulsion parameter—a task that has not been undertaken before. After extracting all the symmetry of the model we found, to our great surprise, many instances of permanent degeneracy of levels with different symmetry and also crossing of levels of the same symmetry. We can also demonstrate that there is no hidden symmetry to account for these effects. Since these results run counter to one of the oldest folk theorems in quantum chemistry, our otherwise uninspiring graphs may be of general interest.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 28 (1972), S. 251-257 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that if Φ is a finite range interaction of a quantum spin system,τ t Φ the associated group of time translations, τ x the group of space translations, andA, B local observables, then $$\mathop {\lim }\limits_{\begin{array}{*{20}c} {|t| \to \infty } \\ {|x| 〉 \upsilon |t|} \\ \end{array} } ||[\tau _t^\Phi \tau _x (A),B]||e^{\mu (\upsilon )t} = 0$$ wheneverv is sufficiently large (v〉VΦ) where μ(v)〉0. The physical content of the statement is that information can propagate in the system only with a finite group velocity.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 31 (1973), S. 327-340 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We derive a classical integral representation for the partition function,Z Q , of a quantum spin system. With it we can obtain upper and lower bounds to the quantum free energy (or ground state energy) in terms of two classical free energies (or ground state energies). These bounds permit us to prove that when the spin angular momentumJ → ∞ (but after the thermodynamic limit) the quantum free energy (or ground state energy) is equal to the classical value. In normal cases, our inequality isZ C (J)≦Z Q (J)≦Z C (J+1).
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 188 (1997), S. 499-500 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 12 (1986), S. 57-69 
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It has been argued that the spectra of infinite length, translation and U(1) invariant, anisotropic, antiferromagnetic spin s chains differ according to whether s is integral or 1/2 integral: There is a range of parameters for which there is a unique ground state with a gap above it in the integral case, but no such range exists for the 1/2 integral case. We prove the above statement for 1/2 integral spin. We also prove that for all s, finite length chains have a unique ground state for a wide range of parameters. The argument was extended to SU(n) chains, and we prove analogous results in that case as well.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 22 (1991), S. 145-154 
    ISSN: 1573-0530
    Keywords: 81R30 ; 81S30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We introduce a technique to compare different, but related, quantum systems, thereby generalizing the way that coherent states are used to compare quantum systems to classical systems in semiclassical analysis. We then use this technique to estimate the dependence of the free energy of the quantum Heisenberg model on the spin value, and to estimate the relation between the ferromagnetic and antiferromagnetic free energies.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 12 (1975), S. 291-310 
    ISSN: 1572-9613
    Keywords: Thermodynamic limit ; jellium ; charged particles ; uniform background ; neutral system ; free energy density ; quantum mechanics ; equilibrium statistical mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The thermodynamic limit of the free energy, energy, pressure, and entropy is established for a neutral system of charged particles interacting with a fixed, uniformly charged background (jellium).
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 24 (1981), S. 279-297 
    ISSN: 1572-9613
    Keywords: Third law ; entropy ; thermodynamics ; lattice systems ; statistical mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The third law of thermodynamics, in the sense that the entropy per unit volume goes to zero as the temperature goes to zero, is investigated within the framework of statistical mechanics for quantum and classical lattice models. We present two main results: (i) For all models the question of whether the third law is satisfied can be decided completely in terms of ground-state degeneracies alone, provided these are computed for all possible “boundary conditions.” In principle, there is no need to investigate possible entropy contributions from low-lying excited states, (ii) The third law is shown to hold for ferromagnetic models by an analysis of the ground states.
    Type of Medium: Electronic Resource
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