# Bose-Einstein condensation for two dimensional bosons in the Gross-Pitaevskii regime

Serena Cenatiempo (GSSI)
Mathematics Seminar
Tuesday, 9 June, 2020, at 16:15, via zoom (see seminar series homepage)
Description:

We consider systems of N bosons trapped in a two-dimensional box with volume one, interacting through a repulsive potential with scattering length exponentially small in N. We show that in this scaling, known as the two dimensional Gross-Pitaevskii regime, low-energy states exhibit Bose-Einstein condensation with an explicit (optimal, up to logarithmic corrections) bound on the number of orthogonal excitations. The main challenge to be overcome is that in the two dimensional Gross-Pitaevskii regime correlations among the particles are so strong that the ratio between the integral of the potential and the effective coupling appearing in the expressions for the thermodynamic functions is of order N. Joint work with C. Caraci and B. Schlein.