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Binding, Stability, and Non-binding of Multi-polaron Systems

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert and Thomas, Lawrence E. (2011) Binding, Stability, and Non-binding of Multi-polaron Systems. In: Mathematical Results in Quantum Physics. World Scientific , Singapore, pp. 21-32. ISBN 9789814350365. https://resolver.caltech.edu/CaltechAUTHORS:20170501-075001254

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Abstract

The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U = 2ɑ, where U is the electronic Coulomb repulsion and ɑ is the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. We also discuss the Pekar-Tomasevich approximation to the ground state energy, which is valid for large ɑ. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1142/9789814350365_0002DOIArticle
http://www.worldscientific.com/doi/abs/10.1142/9789814350365_0002PublisherArticle
https://arxiv.org/abs/1010.0737arXivDiscussion Paper
Additional Information:© 2010 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Partial financial support from the U.S. National Science Foundation through grants PHY-0965859 (E.L.) and PHY-0845292 (R.S.) are gratefully acknowledged. L.T. would like to thank the PIMS Institute, University of British Columbia, for their hospitality and support.
Funders:
Funding AgencyGrant Number
NSFPHY-0965859
NSFPHY-0845292
University of British ColumbiaUNSPECIFIED
Subject Keywords:Polaron; binding energies; stability; Coulomb system; Lieb-Thirring inequality
Record Number:CaltechAUTHORS:20170501-075001254
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170501-075001254
Official Citation:RUPERT L. FRANK, ELLIOTT H. LIEB, ROBERT SEIRINGER, and LAWRENCE E. THOMAS (2011) BINDING, STABILITY, AND NON-BINDING OF MULTI-POLARON SYSTEMS. Mathematical Results in Quantum Physics: pp. 21-32. DOI: http://dx.doi.org/10.1142/9789814350365_0002
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77084
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:01 May 2017 16:34
Last Modified:03 Oct 2019 17:53

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