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Optimal rate of
condensation for trapped bosons in the Gross–Pitaevskii
regime
Phan Thành Nam, Marcin Napiórkowski, Julien Ricaud and Arnaud Triay |
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Vol. 15 (2022), No. 6, 1585–1616
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Abstract |
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We study the Bose–Einstein condensates of trapped Bose gases in the Gross–Pitaevskii regime. We show that the ground state energy and ground states of the many-body quantum system are correctly described by the Gross–Pitaevskii equation in the large particle number limit, and provide the optimal convergence rate. Our work extends the previous results of Lieb, Seiringer and Yngvason on the leading-order convergence, and of Boccato, Brennecke, Cenatiempo and Schlein on the homogeneous gas. Our method relies on the idea of “completing the square”, inspired by recent works of Brietzke, Fournais and Solovej on the Lee–Huang–Yang formula, and a general estimate for Bogoliubov quadratic Hamiltonians on Fock space. |
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Keywords
trapped Bose gases, Gross–Pitaevskii equation,
Bose–Einstein condensation, optimal bounds
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Mathematical Subject Classification
Primary: 81V70, 81V73
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Milestones
Received: 7 July 2020
Revised: 3 December 2020
Accepted: 10 February 2021
Published: 10 November 2022
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Authors |
| Phan Thành Nam | |
| Department of Mathematics Ludwig Maximilian University of Munich Munich Germany |
Munich Center for Quantum Science
and Technology Munich Germany |
| Marcin Napiórkowski | |
| Department of Mathematical Methods
in Physics Faculty of Physics University of Warsaw Warsaw Poland |
|
| Julien Ricaud | |
| Department of Mathematics Ludwig Maximilian University of Munich Munich Germany |
Munich Center for Quantum Science
and Technology Munich Germany |
| Arnaud Triay | |
| Department of Mathematics Ludwig Maximilian University of Munich Munich Germany |
Munich Center for Quantum Science
and Technology Munich Germany |
