Abstract: Below a critical temperature, interacting Bose gases are expected to exhibit a phase transition to a Bose-Einstein condensate, where collective behavior emergesfrom the underlying many-body theory. At zero temperature, we have precise information on the ground-state energy and the lowlying excitation spectrum in certain scaling limits. Much less is known at temperatures comparable to the critical temperature of the ideal gas. In this talk I will discuss the zerotemperature results as background, then focus on variational constructions of correlated trial states in the Gross–Pitaevskii and thermodynamic limits. I will explain how the con- densate, thermal excitations, and short-range correlations enter these constructions and lead to upper bounds on the free energy. This talk is based on joint work with Giulia Basti, Serena Cenatiempo, Andreas Deuchert.
Il seminario si svolgerà in presenza presso il Dipartimento di Matematica e Fisica, Largo San Leonardo Murialdo, 1 - aula B308.
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