Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble
arXiv:2007.15661 · doi:10.1103/PhysRevResearch.2.043206
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.
arXiv comment17 pages, 4 figures. Cross-references added. For associated code and data repository see: https://github.com/DelMaestroGroup/CanonicalEnsembleTheory-paper-code
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