Binding of polarons and atoms at threshold
Frank, Rupert L
Lieb, Élliott H
Robert Seiringer
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 explode? 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.
Springer
2012
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.ista.ac.at/record/2400
Frank R, Lieb É, Seiringer R. Binding of polarons and atoms at threshold. <i>Communications in Mathematical Physics</i>. 2012;313(2):405-424. doi:<a href="https://doi.org/10.1007/s00220-012-1436-9">10.1007/s00220-012-1436-9</a>
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00220-012-1436-9
info:eu-repo/semantics/openAccess