Open Access
2019 Gross–Pitaevskii dynamics for Bose–Einstein condensates
Christian Brennecke, Benjamin Schlein
Anal. PDE 12(6): 1513-1596 (2019). DOI: 10.2140/apde.2019.12.1513


We study the time-evolution of initially trapped Bose–Einstein condensates in the Gross–Pitaevskii regime. We show that condensation is preserved by the many-body evolution and that the dynamics of the condensate wave function can be described by the time-dependent Gross–Pitaevskii equation. With respect to previous works, we provide optimal bounds on the rate of condensation (i.e., on the number of excitations of the Bose–Einstein condensate). To reach this goal, we combine the method of Lewin, Nam and Schlein (2015), who analyzed fluctuations around the Hartree dynamics for N-particle initial data in the mean-field regime, with ideas of Benedikter, de Oliveira and Schlein (2015), who considered the evolution of Fock-space initial data in the Gross–Pitaevskii regime.


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Christian Brennecke. Benjamin Schlein. "Gross–Pitaevskii dynamics for Bose–Einstein condensates." Anal. PDE 12 (6) 1513 - 1596, 2019.


Received: 15 March 2018; Revised: 26 June 2018; Accepted: 25 October 2018; Published: 2019
First available in Project Euclid: 12 March 2019

zbMATH: 07061133
MathSciNet: MR3921312
Digital Object Identifier: 10.2140/apde.2019.12.1513

Primary: 35Q40 , 81V70

Keywords: Bose–Einstein condensates , Gross–Pitaevskii equation , quantum dynamics

Rights: Copyright © 2019 Mathematical Sciences Publishers

Vol.12 • No. 6 • 2019
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