: Bose-Einstein condensation (BEC) is a special phenomenon of trapped Bose gases at low temperatures where a macroscopic fraction of the particles occupies the same one-particle quantum state, called condensate. The rigorous mathematical understanding of this phenomenon remains an on-going challenge in mathematical physics. This talk concerns a probabilistic approach to BEC: We consider the ground state of an interacting Bose gas on the three-dimensional unit torus, known to exhibit BEC. Bounded one-particle operators with law given through the ground state correspond to correlated random variables due to the particles’ interaction. For weak interactions in the mean-field regime, we show that bounded one-particle operators satisfy large deviation estimates and compute the rate function up to second order. For singular interactions in the Gross-Pitaevskii regime, we prove an upper bound for large deviations of the quantum depletion, the operator counting the number of particles outside the condensate, based on an explicit asymptotic formula its generating function. The talk is based on joint works with Nils Behrmann, Christian Brennecke and Phan Thanh Nam.
Back to Workshop I: Optimal Transport for Density Operators: Theory and Numerics
Copyright. All Rights Reserved.