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Focusing dynamics of
2D Bose gases in the instability regime
Lea Boßmann, Charlotte Dietze and Phan Thành Nam |
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Vol. 19 (2026), No. 2, 281–316
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Abstract |
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We consider the dynamics of a 2D Bose gas with an interaction potential of the form for . 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 -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. |
Keywords
Bose–Einstein condensate, effective evolution equations,
focusing NLS
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Mathematical Subject Classification
Primary: 35Q55, 81V73
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Milestones
Received: 14 February 2024
Revised: 2 December 2024
Accepted: 2 February 2025
Published: 22 January 2026
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Authors |
| Lea Boßmann | |
| Department of Mathematics Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen Germany |
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| Charlotte Dietze | |
| Laboratoire Jacques-Louis
Lions Sorbonne Université CNRS Paris France |
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| Phan Thành Nam | |
| Department of Mathematics Ludwig Maximilian University of Munich Munich Germany |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
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