PhD Defense ved Robin Reuvers

Title: Analysis of the Bogoliubov free energy functional

Einstein's classic description of non-interacting bosons predicts at what temperature the phase transition to Bose-Einstein condensation occurs, but how this critical temperature changes when the bosons start to interact weakly is an old problem. To study this question, we analyse a variational reformulation of the Bogoliubov approximation that is commonly used to describe weakly-interacting Bose gases. I will describe several aspects of the resulting model: its derivation, the existence of minimizers, the phase diagram, and finally the critical temperature, which has the form predicted by Lee and Yang in 1958 and a constant that agrees with numerical simulations.

 Supervisor:

 Prof. Jan Philip Solovej

Assessment committee:

Prof. Bergfinnur Durhuus, Math, Chairman, University of Copenhagen

Prof. Søren Fournais, Aarhus University

Ass. Prof. Daniel Ueltschi, University of Warwick