Free Energy of a Dilute Bose Gas: Lower Bound

Jun Yin

Florian Haberberger, Christian Hainzl, Benjamin Schlein +1 more

Rudi Weikard, Gilbert Weinstein

Lower Bound, Robert Seiringer, Robert Seiringer

A lower bound is derived on the free energy (per unit volume) of a homogeneous Bose gas at density and temperature T. In the dilute regime, i.e., when a 3 ≪ 1, where a denotes the scattering length of the pair-interaction potential, our bound differs to leading order from the expression for non-interacting particles by the term 4πa(2 2 −[−c] 2 +). Here, c(T) denotes the critical density for Bose-Einstein condensation (for the non-interacting gas), and [ ·]+ = max { · , 0} denotes the positive part. Our bound is uniform in the temperature up to temperatures of the order of the critical temperature, i.e., T ∼ 2/3 or smaller. One of the key ingredients in the proof is the use of coherent states to extend the method introduced in [17] for estimating correlations to temperatures below the critical one. 1 Introduction and Main Result The advance of experimental techniques for studying ultra-cold atomic gases

Søren Fournais, Lukas Junge, Théotime Girardot +3 more

Abstract We consider a dilute Bose gas in the thermodynamic limit and prove a lower bound on the free energy for low temperatures which is in agreement with the conjecture of Lee–Huang–Yang on the excitation spectrum of the system. Combining techniques of Fournais and Solovej (Invent Math 232(2):863–994, 2023) and Haberberger et al. (The free energy of dilute Bose gases at low temperatures, 2023), we give a simpler and shorter proof resolving the case of strong interactions, including the hard-core potential.

Florian Haberberger