Vol. 14, No. 7, 2021

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The Landau–Pekar equations: adiabatic theorem and accuracy

Nikolai Leopold, Simone Rademacher, Benjamin Schlein and Robert Seiringer

Vol. 14 (2021), No. 7, 2079–2100
Abstract

We prove an adiabatic theorem for the Landau–Pekar equations. This allows us to derive new results on the accuracy of their use as effective equations for the time evolution generated by the Fröhlich Hamiltonian with large coupling constant α. In particular, we show that the time evolution of Pekar product states with coherent phonon field and the electron being trapped by the phonons is well approximated by the Landau–Pekar equations until times short compared to α2.

Keywords
polaron, dynamics, adiabatic theorem
Mathematical Subject Classification 2010
Primary: 35Q40, 46N50
Milestones
Received: 9 May 2019
Revised: 2 March 2020
Accepted: 22 April 2020
Published: 10 November 2021
Authors
Nikolai Leopold
Institute of Science and Technology Austria
Klosterneuburg
Austria
Department of Mathematics and Computer Science
University of Basel
Basel
Switzerland
Simone Rademacher
Institute of Mathematics
University of Zurich
Zurich
Switzerland
Institute of Science and Technology Austria
Klosterneuburg
Austria
Benjamin Schlein
Institute of Mathematics
University of Zurich
Zurich
Switzerland
Robert Seiringer
Institute of Science and Technology Austria
Klosterneuburg
Austria