Many-body density of states of bosonic and fermionic gases: a combinatorial approach

TL;DR

This paper derives exact formulas for the many-body density of states of bosonic and fermionic gases using combinatorial methods, revealing a surprising equivalence and a particle-number independent regime.

Contribution

It introduces a combinatorial approach to exactly compute the density of states and uncovers a mapping showing fermionic and bosonic gases share the same density of states up to an energy shift.

Findings

Fermionic and bosonic gases have identical many-body density of states up to a shift.

A regime exists where the density of states is independent of particle number.

The approach provides exact expressions valid for equally spaced spectra.

Abstract

We use a combinatorial approach to obtain exact expressions for the many-body density of states of fermionic and bosonic gases with equally spaced single-particle spectra. We identify a mapping that reveals a remarkable property, namely, fermionic and bosonic gases have the same many-body density of states, up to a shift corresponding to ground state energy. Additionally, we show that there is a regime, comprising the validity range of the Bethe approximation, where the many-body density of states becomes independent of the number of particles.