06/02/2024: Marco Olivieri @ PoliMi

Tuesday, February 6, 2024 – 14:15
Sala Consiglio
Dipartimento di Matematica
Politecnico di Milano
Ed. 14 “Nave”, Campus Leonardo

SPEAKER: Marco Olivieri (University of Copenhagen)

A novel method for the derivation of the free energy expansion of the Bose gases

We present an innovative method to derive the expansion of the free energy
density of a dilute Bose gas in thermodynamic regime in dimension three. In the first part of the talk, we give a gentle introduction on the thermodynamic limit as the optimal tool for the macroscopic derivation of the thermodynamics from the quantum statistical mechanics. In the second part of the talk, we will focus our attention on the macroscopic behavior of Bose gases, which have a phase transition to Bose Einstein condensates for low temperature. We then study a gas of many bosons interacting through a spherical, pairwise, positive potential. Using a combination of the renormalization of the potential, the Neumann localization and Bogoliubov diagonalization, we derive a lower bound for the second order expansion of the free energy.

This initiative is part of the “PhD Lectures” activity of the project “Departments of Excellence 2023-2027” of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on thetopics presented at the talk.