Modul: MAT675 PDE and Mathematical Physics

## Third order corrections to the ground state energy of a Bose gas in the Gross-Pitaevskii regime.

Talk by Cristina Caraci

**Date:** 11.04.24 **Time:** 16.15 - 18.00 **Room:** Y27H46

We consider a system of N bosons confined in a unit box with periodic boundary conditions. We assume that the particles interact through a repulsive two-boxy potential with scattering length of order 1/N, i.e. the Gross-Pitaevskii regime. We establish a precise bound for the ground state energy E(N) of the system. While the leading contribution, of order N, to the energy has been known since the pioneering works of Lieb-Seiringer-Yngvason in the early 2000s, and the second order (of order one) corrections were more recently first determined by Boccato-Brennecke-Cenatiempo-Schlein, our estimate also resolves the next term in the asymptotic expansion of E(N), which is of the order (log N)/N, confirming Wu’s predictions in 1959. Based on a joint work with Alessandro Olgiati, Diane Saint Aubin and Benjamin Schlein.''