Occupation numbers in a quantum canonical ensemble: a projection operator approach

TL;DR

This paper extends a projection operator method to accurately compute occupation numbers and chemical potentials in the canonical ensemble, addressing numerical challenges for fermions and bosons in quantum statistical physics.

Contribution

It provides a novel extension of the projector formalism to directly calculate occupation numbers and chemical potentials in the canonical ensemble.

Findings

Successful extension of the formalism to occupation numbers and chemical potential.

Resolution of numerical instability issues for fermions.

Applicability to both fermionic and bosonic systems.

Abstract

Recently, we have used a projection operator to fix the number of particles in a second quantization approach in order to deal with the canonical ensemble. Having been applied earlier to handle various problems in nuclear physics that involve fixed particle numbers, the projector formalism was extended to grant access as well to quantum-statistical averages in condensed matter physics, such as particle densities and correlation functions. In this light, the occupation numbers of the subsequent single-particle energy eigenstates are key quantities to be examined. The goal of this paper is 1) to provide a sound extension of the projector formalism directly addressing the occupation numbers as well as the chemical potential, and 2) to demonstrate how the emerging problems related to numerical instability for fermions can be resolved to obtain the canonical statistical quantities for both fermions and bosons.