The zeros and poles of the partition function

TL;DR

This paper explores the physical significance of zeros and poles of the partition function across different systems, including quantum, mathematical, and astrophysical contexts.

Contribution

It introduces a unified perspective on the zeros and poles of the partition function in diverse physical and mathematical systems.

Findings

Identifies the role of zeros and poles in the harmonic oscillator.

Analyzes the zeros and poles of the Riemann zeta function.

Examines the quasinormal modes of black holes.

Abstract

In this paper, we consider the physical meaning of the zeros and poles of partition function. We consider three different systems, including the harmonic oscillator in one dimension, Riemann zeta function and the quasinormal modes of black hole.