Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 1871–2245
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
This article is available for purchase or by subscription. See below.
Optimal rate of condensation for trapped bosons in the Gross–Pitaevskii regime

Phan Thành Nam, Marcin Napiórkowski, Julien Ricaud and Arnaud Triay

Vol. 15 (2022), No. 6, 1585–1616
Abstract

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.

PDF Access Denied

We have not been able to recognize your IP address 3.238.116.201 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
trapped Bose gases, Gross–Pitaevskii equation, Bose–Einstein condensation, optimal bounds
Mathematical Subject Classification
Primary: 81V70, 81V73
Milestones
Received: 7 July 2020
Revised: 3 December 2020
Accepted: 10 February 2021
Published: 10 November 2022
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