GENERALIZED THERMAL ZETA-FUNCTIONS

TL;DR

This paper generalizes the calculation of thermal zeta-functions for harmonic oscillators with quasi-periodic boundary conditions, extending previous work and proposing new analytic methods, with potential implications for anyonic systems.

Contribution

It introduces a generalized approach to thermal zeta-functions for harmonic oscillators, encompassing bosonic, fermionic, and quasi-periodic cases, along with an alternative analytic extension method.

Findings

Derived a generalized partition function for quasi-periodic harmonic oscillators.

Provided an alternative analytic continuation for the Epstein function.

Suggested a possible connection to anyonic systems.

Abstract

We calculate the partition function of a harmonic oscillator with quasi-periodic boundary conditions using the zeta-function method. This work generalizes a previous one by Gibbons and contains the usual bosonic and fermionic oscillators as particular cases. We give an alternative prescription for the analytic extension of the generalized Epstein function involved in the calculation of the generalized thermal zeta-functions. We also conjecture about the relation of our calculation to anyonic systems.