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In this 42-minute lecture, explore the mathematical challenges of Bose-Einstein condensation (BEC) through a probabilistic approach with Simone Rademacher from Ludwig-Maximilians-Universität München. Recorded at IPAM's Optimal Transport for Density Operators workshop at UCLA, discover how BEC occurs when a macroscopic fraction of particles in trapped Bose gases at low temperatures occupy the same one-particle quantum state. Learn about large deviation estimates for bounded one-particle operators in weakly interacting systems in the mean-field regime, and examine upper bounds for large deviations of quantum depletion in the Gross-Pitaevskii regime with singular interactions. The presentation covers joint research with Nils Behrmann, Christian Brennecke, and Phan Thanh Nam, offering valuable insights into this ongoing challenge in mathematical physics.
