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

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.