Critical point of the two-dimensional Bose gas: an S-matrix approach

TL;DR

This paper introduces a novel S-matrix based approach to determine the critical temperature of the two-dimensional interacting Bose gas, providing a new formalism reminiscent of the thermodynamic Bethe ansatz.

Contribution

It develops a new formulation for interacting gases at finite density and temperature using the S-matrix, leading to an analytical expression for the critical temperature.

Findings

Derived an approximate critical temperature formula for 2D Bose gas

Established a formalism connecting thermodynamics with the 2-body S-matrix

Presented an integral equation for the pseudo-energy based on the S-matrix kernel

Abstract

A new treatment of the critical point of the two-dimensional interacting Bose gas is presented. In the lowest order approximation we obtain the critical temperature T_c ~ 2 \pi n/[ m \log (2\pi/mg)], where n is the density, m the mass, and g the coupling. This result is based on a new formulation of interacting gases at finite density and temperature which is reminiscent of the thermodynamic Bethe ansatz in one dimension. In this formalism, the basic thermodynamic quantities are expressed in terms of a pseudo-energy. Consistent resummation of 2-body scattering leads to an integral equation for the pseudo-energy with a kernel based on the logarithm of the exact 2-body S-matrix.