On the Theory of Superfluidity in Two Dimensions

TL;DR

This paper investigates the superfluid phase transition in two-dimensional vortex gases, establishing conditions for superfluidity, deriving the transition temperature, and providing bounds and exact expressions for vortex densities.

Contribution

It extends the theory of superfluidity to include vortices with arbitrary circulation and derives key properties of the vortex gas at the transition.

Findings

Superfluid phase exists only when net vortex circulation is zero.

Transition temperature equals the Kosterlitz-Thouless temperature.

Derived bounds and exact expressions for vortex densities.

Abstract

The superfluid phase transition of the general vortex gas, in which the circulations may be any non-zero integer, is studied. When the net circulation of the system is not zero the absence of a superfluid phase is shown. When the net circulation of the vortices vanishes, the presence of off-diagonal long range order is demonstrated and the existence of an order parameter is proposed. The transition temperature for the general vortex gas is shown to be the Kosterlitz---Thouless temperature. An upper bound for the average vortex number density is established for the general vortex gas and an exact expression is derived for the Kosterlitz---Thouless ensemble.