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The periodic Lieb-Thirring inequality

Frank, Rupert L. and Gontier, David and Lewin, Mathieu (2020) The periodic Lieb-Thirring inequality. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20211004-222655493

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Abstract

We discuss the Lieb-Thirring inequality for periodic systems, which has the same optimal constant as the original inequality for finite systems. This allows us to formulate a new conjecture about the value of its best constant. To demonstrate the importance of periodic states, we prove that the 1D Lieb-Thirring inequality at the special exponent γ = 3/2 admits a one-parameter family of periodic optimizers, interpolating between the one-bound state and the uniform potential. Finally, we provide numerical simulations in 2D which support our conjecture that optimizers could be periodic.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2010.02981arXivDiscussion Paper
ORCID:
AuthorORCID
Frank, Rupert L.0000-0001-7973-4688
Gontier, David0000-0001-8648-7910
Lewin, Mathieu0000-0002-1755-0207
Additional Information:This project has received funding from the U.S. National Science Foundation (grant agreements DMS-1363432 and DMS-1954995 of R.L.F.) and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement MDFT 725528 of M.L.).
Funders:
Funding AgencyGrant Number
NSFDMS-1363432
NSFDMS-1954995
European Research Council (ERC)725528
Subject Keywords:Lieb-Thirring inequality, periodic Schr¨odinger operators
Classification Code:Mathematics Subject Classification 2020. Primary 81Q10
Record Number:CaltechAUTHORS:20211004-222655493
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20211004-222655493
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111197
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:04 Oct 2021 22:59
Last Modified:04 Oct 2021 22:59

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