Binding of Polarons and Atoms at Threshold
Abstract
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.
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.Attached Files
Submitted - 1106.0729.pdf
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Additional details
- Eprint ID
- 77095
- Resolver ID
- CaltechAUTHORS:20170501-091837793
- PHY-0965859
- NSF
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Created
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2017-05-01Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field