Thermodynamically Equivalent Hamiltonian for Some Many-Body Problems

Abstract

A method which allows a rigorous treatment of the statistical mechanics of a superconductor (Bardeen-Cooper-Schrieffer model) is generalized so as to be applicable to a wider class of many-fermion or many-boson systems.As an illustration, we study a degenerate boson gas, adopting the "pair Hamiltonian" of Girardeau and Arnowitt. We confirm their finding, for this model, that there is a "gap" in the energy spectrum of the lowest excitations.