About

I am interested in the rigorous study of quantum mechanical models and their derivation from first principles. In quantum mechanics, the numerical treatment of systems with large number of particles is very challenging. One relies instead on effective models which are easier to solve. It is therefore important to know their domain of validity and the correct coupling constants within.

In this project, I am part of project A4 whose goal is to rigorously investigate the correlation structure of large bosonic systems in the dilute regime. In such a system, at low enough temperature, a macroscopic fraction of the particles occupy the same quantum state, forming a Bose-Einstein condensate. In a famous paper, Lee, Huang and Yang described the fluctuations around the condensate as quasi-particles behaving as independent quantum oscillators following Bogoliubov’s dispersion relation. Our main objective is to prove the validity of this picture.