FOCUSING DYNAMICS OF 2D BOSE GASES IN THE INSTABILITY REGIME

Boßmann L, Dietze C, Nam PT (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Analysis & Pde

Book Volume: 19

Pages Range: 281-316

Journal Issue: 2

DOI: 10.2140/apde.2026.19.281

Abstract

We consider the dynamics of a 2D Bose gas with an interaction potential of the form N2β-1w(Nβ∙) for β ϵ (0,3/2). The interaction may be chosen to be negative and large, leading to the instability regime where the corresponding focusing cubic nonlinear Schrödinger equation (NLS) may blow up in finite time. We show that to leading order, the N-body quantum dynamics can be effectively described by the NLS prior to the blow-up time. Moreover, we prove the validity of the Bogoliubov approximation, where the excitations from the condensate are captured in a norm approximation of the many-body dynamics.

Authors with CRIS profile

Lea Boßmann Professur für Mathematik (Analysis)

Involved external institutions

Sorbonne Université FR France (FR) Ludwig-Maximilians-Universität (LMU) DE Germany (DE)

How to cite

APA:

Boßmann, L., Dietze, C., & Nam, P.T. (2026). FOCUSING DYNAMICS OF 2D BOSE GASES IN THE INSTABILITY REGIME. Analysis & Pde, 19(2), 281-316. https://doi.org/10.2140/apde.2026.19.281

MLA:

Boßmann, Lea, Charlotte Dietze, and Phan Thành Nam. "FOCUSING DYNAMICS OF 2D BOSE GASES IN THE INSTABILITY REGIME." Analysis & Pde 19.2 (2026): 281-316.

BibTeX: Download