---
_id: '2400'
abstract:
- lang: eng
text: 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.
author:
- first_name: Rupert
full_name: Frank, Rupert L
last_name: Frank
- first_name: Élliott
full_name: Lieb, Élliott H
last_name: Lieb
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Frank R, Lieb É, Seiringer R. Binding of polarons and atoms at threshold. *Communications
in Mathematical Physics*. 2012;313(2):405-424. doi:10.1007/s00220-012-1436-9
apa: Frank, R., Lieb, É., & Seiringer, R. (2012). Binding of polarons and atoms
at threshold. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-012-1436-9
chicago: Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Binding of Polarons
and Atoms at Threshold.” *Communications in Mathematical Physics*. Springer,
2012. https://doi.org/10.1007/s00220-012-1436-9.
ieee: R. Frank, É. Lieb, and R. Seiringer, “Binding of polarons and atoms at threshold,”
*Communications in Mathematical Physics*, vol. 313, no. 2. Springer, pp.
405–424, 2012.
ista: Frank R, Lieb É, Seiringer R. 2012. Binding of polarons and atoms at threshold.
Communications in Mathematical Physics. 313(2), 405–424.
mla: Frank, Rupert, et al. “Binding of Polarons and Atoms at Threshold.” *Communications
in Mathematical Physics*, vol. 313, no. 2, Springer, 2012, pp. 405–24, doi:10.1007/s00220-012-1436-9.
short: R. Frank, É. Lieb, R. Seiringer, Communications in Mathematical Physics 313
(2012) 405–424.
date_created: 2018-12-11T11:57:27Z
date_published: 2012-07-01T00:00:00Z
date_updated: 2021-01-12T06:57:15Z
day: '01'
doi: 10.1007/s00220-012-1436-9
extern: 1
intvolume: ' 313'
issue: '2'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/1106.0729
month: '07'
oa: 1
page: 405 - 424
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4527'
quality_controlled: 0
status: public
title: Binding of polarons and atoms at threshold
type: journal_article
volume: 313
year: '2012'
...