Statistical Theory of 2-Dimensional Quantum Vortex Gas: Non-Canonical Effect and Generalized Zeta Function

TL;DR

This paper develops a quantum statistical framework for 2D vortex gases using generalized Hamiltonian dynamics, revealing connections to the generalized Riemann zeta function and topological phase transitions.

Contribution

It introduces a novel quantum statistical theory for vortex gases based on generalized Hamiltonian dynamics and links the partition function to the generalized Riemann zeta function.

Findings

Partition function expressed via generalized Riemann zeta function

Topological phase transition related to zeta function poles

Quantized spectrum derived for vortex pairs

Abstract

The purpose of this paper is to present a quantum statistical theory of 2-dimensional vortex gas based on the generalized Hamiltonian dynamics recently developed. The quantized spectrum is evaluated for a pair of vortex on the basis of the semiclassical quantization rule. This is used to evaluate the partition function for a dilute vortex gas. A remarkable consequence is that the partition function and related quantities are given in terms of the generalized Riemann zeta function. The topological phase transition is naturally understood as the pole structure of the zeta function.