AG Mathematische Physik, Phan Thành Nam (LMU): Bogoliubov-Lee-Yang theory for the mean-field Bose gas at positive temperatures

Phan Thành Nam (LMU)

Bogoliubov-Lee-Yang theory for the mean-field Bose gas at positive temperatures

Abstract: I will discuss recent joint work with Andreas Deuchert and
Marcin Napiórkowski on the rigorous justification of a version of
Bogoliubov theory proposed by Lee and Yang in 1958 to describe the
interacting Bose gas at positive temperatures, comparable to the
critical temperature of the Bose-Einstein phase transition. We consider
the homogeneous mean-field Bose gas on the 3D torus and prove a
trace-norm approximation for the grand canonical Gibbs state, which also
yields precise formulas for correlation functions. Our result goes
beyond the standard quasi-free approximation, and a key ingredient of
our proof is an abstract correlation inequality based on Stahl’s
theorem.