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A non-linear adiabatic theorem for the one-dimensional Landau–Pekar equations

Frank, Rupert L. and Gang, Zhou (2020) A non-linear adiabatic theorem for the one-dimensional Landau–Pekar equations. Journal of Functional Analysis, 279 (7). Art. No. 108631. ISSN 0022-1236.

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We discuss a one-dimensional version of the Landau–Pekar equations, which are a system of coupled differential equations with two different time scales. We derive an approximation on the slow time scale in the spirit of a non-linear adiabatic theorem. Dispersive estimates for solutions of the Schrödinger equation with time-dependent potential are a key technical ingredient in our proof.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Frank, Rupert L.0000-0001-7973-4688
Gang, Zhou0000-0002-1649-1823
Additional Information:© 2020 Elsevier Inc. Received 20 June 2019, Accepted 28 April 2020, Available online 14 May 2020. The first author would like to thank Benjamin Schlein and Robert Seiringer for interesting discussions. Partial support through US National Science Foundation grant DMS-1363432 and through German Research Foundation grant EXC-2111 390814868 (R.L.F.) is acknowledged.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)EXC-2111 390814868
Subject Keywords:Polaron; Adiabatic theorem; Dispersive estimates
Issue or Number:7
Record Number:CaltechAUTHORS:20200515-091132161
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Official Citation:Rupert L. Frank, Zhou Gang, A non-linear adiabatic theorem for the one-dimensional Landau–Pekar equations, Journal of Functional Analysis, Volume 279, Issue 7, 2020, 108631, ISSN 0022-1236, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103228
Deposited By: Tony Diaz
Deposited On:15 May 2020 16:36
Last Modified:02 Jun 2020 16:07

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