A Caltech Library Service

Binding of Polarons and Atoms at Threshold

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert (2011) Binding of Polarons and Atoms at Threshold. . (Submitted)

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


If the polaron coupling constant α is large enough, bipolarons or multi-polarons will form. When passing through the critical α_c from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explodes? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at α_c. Similarly, we show that the same phenomenon occurs for atoms, e.g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger equation, and are very general. They use the fact that the Coulomb repulsion decays like 1/r, while 'uncertainty principle' localization energies decay more rapidly, as 1/r^2.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription paper
Frank, Rupert L.0000-0001-7973-4688
Lieb, Elliott H.0000-0001-5843-3587
Additional Information:© 2011 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. (Submitted on 3 Jun 2011) We are grateful to Herbert Spohn for making us aware of this problem. Partial financial support from the U.S. National Science Foundation through grant PHY-0965859 (E.L.) and the NSERC (R.S.) is gratefully acknowledged.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Record Number:CaltechAUTHORS:20170501-091837793
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77095
Deposited By: Ruth Sustaita
Deposited On:01 May 2017 16:28
Last Modified:09 Mar 2020 13:19

Repository Staff Only: item control page