PDEA seminar: 1D focusing Bose gases with two- and (critical) attractive three-body interactions

Abstract: We consider a one-dimensional, trapped, focusing Bose gas where $N$ bosons interact with each other via both a scaled two-body interaction potential and an attractive scaled three-body interaction potential. The system is stable if and only if the three-body interaction is not too negative. In the mean-field limit regime, we prove that  the many-body system exhibits the Bose--Einstein condensation on the cubic-quintic NLS ground states. In the collapse regime, we prove that the ground state of the system is fully condensed on the (unique) solution to the quintic NLS equation. We also discuss the case of critical three-body interaction.

This is a seminar in the PDEs and Applications seminar series