Vol. 3, No. 4, 2021

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Landau–Pekar equations and quantum fluctuations for the dynamics of a strongly coupled polaron

Nikolai Leopold, David Mitrouskas, Simone Rademacher, Benjamin Schlein and Robert Seiringer

Vol. 3 (2021), No. 4, 653–676
Abstract

We consider the Fröhlich Hamiltonian with large coupling constant α. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm-approximation of the evolution, valid up to times of order α2. The approximation is given in terms of a Pekar product state, evolved through the Landau–Pekar equations, corrected by a Bogoliubov dynamics taking quantum fluctuations into account. This allows us to show that the Landau–Pekar equations approximately describe the evolution of the electron- and one-phonon reduced density matrices under the Fröhlich dynamics up to times of order α2.

Keywords
polaron dynamics, Landau–Pekar equations, quantum fluctuations, Bogoliubov dynamics
Mathematical Subject Classification
Primary: 35Q40, 46N50
Milestones
Received: 9 December 2020
Revised: 22 April 2021
Accepted: 26 May 2021
Published: 12 February 2022
Authors
Nikolai Leopold
Department of Mathematics and Computer Science
University of Basel
Basel
Switzerland
David Mitrouskas
Institute of Science and Technology Austria
Klosterneuburg
Austria
Simone Rademacher
Institute of Science and Technology Austria
Klosterneuburg
Austria
Benjamin Schlein
Institute of Mathematics
University of Zurich
Zürich
Switzerland
Robert Seiringer
Institute of Science and Technology Austria
Klosterneuburg
Austria