# Talk

Modul:   MAT675  PDE and Mathematical Physics

## The free energy of the two-dimensional dilute Bose gas

Dr. Andreas Deuchert talk

Date: 24.10.19  Time: 18.10 - 19.10  Room: Y27H35/36

We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density ρ and inverse temperature β differs from the one of the non-interacting system by the correction term (4πρ^2/|lna^2ρ|)(2−[1−βc/β]_+^2). Here a is the scattering length of the interaction potential, [⋅]+=max{0,⋅} and βc is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. The result is valid in the dilute limit a^2 ρ≪1 and if βρ≳1. This is joint work with Simon Mayer and Robert Seiringer.