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

摘要

The purpose of this paper is to present a quantum statistical theory of2-dimensional vortex gas based on the generalized Hamiltonian dynamics recentlydeveloped. The quantized spectrum is evaluated for a pair of vortex on thebasis of the semiclassical quantization rule. This is used to evaluate thepartition function for a dilute vortex gas. A remarkable consequence is thatthe partition function and related quantities are given in terms of thegeneralized Riemann zeta function. The topological phase transition isnaturally understood as the pole structure of the zeta function.