Dynamics of mean-field bosons at positive temperature
Andreas Deuchert
University of Zurich, SwitzerlandMarco Caporaletti
University of Zurich, SwitzerlandBenjamin Schlein
University of Zurich, Switzerland
Abstract
We study the time evolution of an initially trapped weakly interacting Bose gas at positive temperature, after the trapping potential has been switched off. It has been recently shown in Deuchert–Seiringer (2021) that the one-particle density matrix of Gibbs states of the interacting trapped gas is given, to leading order in , as , by that of the ideal gas, with the condensate wave function replaced by the minimizer of the Hartree energy functional. We show that this structure is stable with respect to the many-body evolution in the following sense: the dynamics can be approximated in terms of the time-dependent Hartree equation for the condensate wave function and in terms of the free evolution for the thermally excited particles. The main technical novelty of our work is the use of the Hartree–Fock–Bogoliubov equations to define a fluctuation dynamics.
Cite this article
Andreas Deuchert, Marco Caporaletti, Benjamin Schlein, Dynamics of mean-field bosons at positive temperature. Ann. Inst. H. Poincaré Anal. Non Linéaire 41 (2024), no. 4, pp. 995–1054
DOI 10.4171/AIHPC/93