# Ground state energy of a dilute two-dimensional Bose gas from the Bogoliubov free energy functional

## TL;DR

This paper extends the analysis of the Bogoliubov free energy functional to two-dimensional dilute Bose gases at very low temperatures, deriving precise asymptotics for the ground state energy under weak interactions.

## Contribution

It provides the first rigorous derivation of two-term asymptotics for the ground state energy of a 2D dilute Bose gas at low temperatures.

## Key findings

- Derived two-term asymptotics for the ground state energy.
- Extended Bogoliubov analysis to two-dimensional systems.
- Confirmed weak interaction regime results.

## Abstract

We extend the analysis of the Bogoliubov free energy functional to two dimensions at very low temperatures. For sufficiently weak interactions, we prove two term asymptotics for the ground state energy.