Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble

Hatem Barghathi, Jiangyong Yu and Adrian Del Maestro arXiv:2007.15661

Summary

Wick's theorem for degenerate quantum gases in the canonical ensemble

Abstract

We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary partition functions, and represents a unification of previous distinct approaches with many known results appearing as direct consequences of the developed mathematical structure. In addition, we introduce a general decomposition of the correlations between occupation numbers in terms of the occupation numbers of individual energy levels, that is valid for both non-degenerate and degenerate spectra. To demonstrate the applicability of the theory in the presence of degeneracy, we compute energy level correlations up to fourth order in a bosonic ring in the presence of a magnetic field.

Description

This repository includes links, code, scripts, and data to perform numerical calculations and generate figures for the associated paper on deriving a theory for non-interacting fermions and bosons in the canonical ensemble.

Support

The creation of these materials was supported in part by the National Science Foundation under Award No. DMR-1553991.

Figures

Figure 01: The joint probability distribution of two energy levels

Figure 02: Two-points connected correlations (Spinless bosons)

Figure 03: Two-points connected correlations (Spin-1 bosons)

Figure 04: Four-level correlations