The Gibbs State of the Mean-Field Bose Gas

Watch a 50-minute lecture by Andreas Deuchert from Virginia Polytechnic Institute and State University presenting "The Gibbs state of the mean-field Bose gas" at IPAM's Optimal Transport for Density Operators workshop. Recorded on April 3, 2025, this talk explores the homogeneous mean-field Bose gas at temperatures proportional to the critical temperature of its Bose-Einstein condensation phase transition. Learn about trace-norm approximation of the grand canonical Gibbs state using reference states given by convex combinations of coherent states and Gibbs states associated with temperature-dependent Bogoliubov Hamiltonians. Discover how this justifies Bogoliubov theory at positive temperature and examine limiting distributions for condensate particle numbers and formulas for density matrices. The presentation includes novel abstract correlation inequalities and applications of infinite-dimensional Stahl's theorem, representing joint work with Phan Thành Nam and Marcin Napiórkowski.