Regensburg 2022 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 9: Cold Atomic Gases and Superfluids

TT 9.3: Talk

Monday, September 5, 2022, 18:30–18:45, H23

The free energy of the two-dimensional dilute Bose gas — •Andreas Deuchert¹, Simon Mayer², and Robert Seiringer² — ¹University of Zurich, Institute of Mathematics, Zurich, Switzerland — ²Institute of Science and Technology Austria, Klosterneuburg, Austria

We prove bounds for the specific free energy 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 4 π ϱ² | ln(a² ϱ) |⁻¹ (2 − [ 1 −β_c/ β ]₊² ) . Here a is the scattering length of the interaction potential, [x]₊ = max{0, x} and β_c is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit a² ϱ ≪ 1 and if β ϱ 1.