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 (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20211004-222655493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) | ||||||||
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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.). | ||||||||
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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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