Programme

O.24 -- Oral, VCTP-50

Date: Thursday, 7 August 2025

Time: 11:35 - 12:00

2D rotating Bose-Einstein condensation at the critical rotation speed

Dinh Thi NGUYEN (1); Van Duong DINH (2); Nicolas ROUGERIE (2)

(1) University of Science, Vietnam National University Ho Chi Minh City, Vietnam; (2) Ecole Normale Superieure de Lyon & CNRS Lyon, France

We study the minimizers of a magnetic 2D non-linear Schroedinger energy functional in a harmonic trapping potential, describing a rotating Bose-Einstein condensate. In the case of a repulsive interaction potential, we derive an effective Thomas-Fermi-like model in the rapidly rotating limit where the centrifugal force compensates the confinement. The available states are restricted to the lowest Landau level. The coupling constant of the Thomas-Fermi functional is to link the emergence of vortex lattices (the Abrikosov problem). When turning from repulsive to attractive interactions, the system is unstable since there is a balance between kinetic and interaction energies. In the regime where the strength of the interaction approaches a critical value from below, the system collapses to a profile obtained from the (unique) optimizer of a Gagliardo-Nirenberg interpolation inequality. This was established before in the case of fixed rotation frequency. We extend the result to rotation frequencies approaching, or even equal to, the critical frequency at which the centrifugal force compensates the trap. We prove that the blow-up scenario is to leading order unaffected by such a strong deconfinement mechanism. In particular, the blow-up profile remains independent of the rotation frequency.

Presenter: Nguyễn Đình Thi