# Calculation of the critical temperature of a dilute Bose gas in the Bogoliubov approximation

## TL;DR

This paper analytically calculates the critical temperature for the Kosterlitz-Thouless transition in a dilute 2D Bose gas using a variational Bogoliubov approximation, including the logarithmic constant.

## Contribution

It provides the first analytical determination of the transition temperature with the logarithmic constant in a 2D dilute Bose gas.

## Key findings

- Analytical expression for the 2D critical temperature derived.
- Includes the constant in the logarithm for the first time.
- Extends previous 3D calculations to 2D systems.

## Abstract

Following an earlier calculation in 3D, we calculate the 2D critical temperature of a dilute, translation-invariant Bose gas using a variational formulation of the Bogoliubov approximation introduced by Critchley and Solomon in 1976. This provides the first analytical calculation of the Kosterlitz-Thouless transition temperature that includes the constant in the logarithm.