Vol. 3, No. 4, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN (electronic): 2578-5885
ISSN (print): 2578-5893
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
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.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/paa

We have not been able to recognize your IP address 44.192.114.32 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

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