Spectral Equivalence of Bosons and Fermions in One-Dimensional Harmonic Potentials

Abstract

Recently, Schmidt and Schnack (cond-mat/9803151, cond-mat/9810036), following earlier references, reiterate that the specific heat of N non-interacting bosons in a one-dimensional harmonic well equals that of N fermions in the same potential. We show that this peculiar relationship between specific heats results from a more dramatic equivalence between bose and fermi systems. Namely, we prove that the excitation spectrums of such bose and fermi systems are spectrally equivalent. Two complementary proofs are provided, one based on an analysis of the dynamical symmetry group of the N-body system, the other using combinatoric analysis.

Six Pages, No Figures, Submitted to Phys. Rev. A

References in corpus (3)

• Observation of p-wave Threshold Law Using Evaporatively Cooled Fermionic Atoms
• Exploring a quantum degenerate gas of fermionic atoms
• Investigations on finite ideal quantum gases

Cited by in corpus (9)

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• Partition functions and symmetric polynomials
• Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations
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• Thermodynamic Equivalence of Certain Ideal Bose and Fermi Gases
• Fluctuations of the Fermi condensate in ideal gases
• Solution of the two identical ion Penning trap final state
• Nucleons as modified Ising models
• Canonical-grandcanonical ensemble in-equivalence in Fermi systems?