Published October 15, 2020
| Submitted
Journal Article
Open
A non-linear adiabatic theorem for the one-dimensional Landau–Pekar equations
- Creators
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Frank, Rupert L.
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Gang, Zhou
Chicago
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Abstract
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.
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.Attached Files
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Additional details
- Eprint ID
- 103228
- Resolver ID
- CaltechAUTHORS:20200515-091132161
- NSF
- DMS-1363432
- Deutsche Forschungsgemeinschaft (DFG)
- EXC-2111 390814868
- Created
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2020-05-15Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field