Fourier formula for quantum partition functions

TL;DR

This paper introduces a Fourier-based method to transform the complex path integral for quantum partition functions into a more manageable form, enabling new solutions to longstanding quantum statistical problems.

Contribution

It derives a novel Fourier expansion formula for quantum partition functions, simplifying the analysis of complex quantum systems.

Findings

Derived a new Fourier formula for quantum partition functions

Applied the method to Bose-Einstein condensation problems

Facilitated access to previously intractable quantum problems

Abstract

Fourier expansion of the integrand in the path integral formula for the partition function of quantum systems leads to a deterministic expression which, though still quite complex, is easier to process than the original functional integral. It therefore can give access to problems that eluded solution so far. Here we derive the formula; applications to the problem of Bose-Einstein condensation are presented in the papers arXiv:2108.02659 [math-ph] and arXiv:2208.08931 [math-ph].