L'étude de l'éxistence et la discipline des états fondamentaux de condensats de Bose -Einstien

Abstract

This thesis focuses on the existence and mass concentration behavior of minimizers for rotating Bose-Einstein condensates (BEC) with attractive interactions in a bounded domain D⊂R^ 2 . It is shown that there exists a finite constant a^* , representing primarily the critical number of bosons in the system, such that the minimal energy e(a) admits minimizers if and only if 0<a<a ^∗ , regardless of the trapping potential V(x) and the rotation speed Ω≥0. This result stands in stark contrast to the case of rotating BECs in the entire plane, where the existence of minimizers depends on the value of Ω Ω. Furthermore, by establishing precise estimates for the rotational term and the minimal energy, we also analyze the mass concentration behavior of the minimizers under a harmonic potential as a↗a