{"publist_id":"4527","publication":"Communications in Mathematical Physics","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","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.","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.","short":"R. Frank, É. Lieb, R. Seiringer, Communications in Mathematical Physics 313 (2012) 405–424.","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","ista":"Frank R, Lieb É, Seiringer R. 2012. Binding of polarons and atoms at threshold. Communications in Mathematical Physics. 313(2), 405–424.","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."},"title":"Binding of polarons and atoms at threshold","_id":"2400","type":"journal_article","publication_status":"published","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1106.0729"}],"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."}],"day":"01","status":"public","extern":1,"issue":"2","intvolume":" 313","author":[{"last_name":"Frank","full_name":"Frank, Rupert L","first_name":"Rupert"},{"last_name":"Lieb","first_name":"Élliott","full_name":"Lieb, Élliott H"},{"full_name":"Robert Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"publisher":"Springer","page":"405 - 424","year":"2012","quality_controlled":0,"date_published":"2012-07-01T00:00:00Z","date_created":"2018-12-11T11:57:27Z","date_updated":"2021-01-12T06:57:15Z","oa":1,"volume":313,"doi":"10.1007/s00220-012-1436-9","month":"07"}