AG Mathematische Physik, Simone Rademacher (LMU München): Large deviations for Bose-Einstein condensates

Simone Rademacher (LMU München)

Large
deviations for Bose-Einstein condensates

Abstract: 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. 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. 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 the tails 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.