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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 (Unpublished)

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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 Paper
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.).
Funding AgencyGrant Number
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:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111197
Deposited By: George Porter
Deposited On:04 Oct 2021 22:59
Last Modified:04 Oct 2021 22:59

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