{"main_file_link":[{"url":"http://arxiv.org/abs/1106.0729","open_access":"1"}],"extern":1,"volume":313,"publisher":"Springer","citation":{"short":"R. Frank, É. Lieb, R. Seiringer, Communications in Mathematical Physics 313 (2012) 405–424.","ieee":"R. Frank, É. Lieb, and R. Seiringer, “Binding of polarons and atoms at threshold,” <i>Communications in Mathematical Physics</i>, vol. 313, no. 2. Springer, pp. 405–424, 2012.","chicago":"Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Binding of Polarons and Atoms at Threshold.” <i>Communications in Mathematical Physics</i>. Springer, 2012. <a href=\"https://doi.org/10.1007/s00220-012-1436-9\">https://doi.org/10.1007/s00220-012-1436-9</a>.","ama":"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>","apa":"Frank, R., Lieb, É., &#38; Seiringer, R. (2012). Binding of polarons and atoms at threshold. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-012-1436-9\">https://doi.org/10.1007/s00220-012-1436-9</a>","mla":"Frank, Rupert, et al. “Binding of Polarons and Atoms at Threshold.” <i>Communications in Mathematical Physics</i>, vol. 313, no. 2, Springer, 2012, pp. 405–24, doi:<a href=\"https://doi.org/10.1007/s00220-012-1436-9\">10.1007/s00220-012-1436-9</a>.","ista":"Frank R, Lieb É, Seiringer R. 2012. Binding of polarons and atoms at threshold. Communications in Mathematical Physics. 313(2), 405–424."},"month":"07","publication":"Communications in Mathematical Physics","publist_id":"4527","type":"journal_article","publication_status":"published","abstract":[{"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.","lang":"eng"}],"oa":1,"status":"public","date_published":"2012-07-01T00:00:00Z","title":"Binding of polarons and atoms at threshold","author":[{"first_name":"Rupert","last_name":"Frank","full_name":"Frank, Rupert L"},{"first_name":"Élliott","last_name":"Lieb","full_name":"Lieb, Élliott H"},{"full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"date_updated":"2021-01-12T06:57:15Z","date_created":"2018-12-11T11:57:27Z","doi":"10.1007/s00220-012-1436-9","quality_controlled":0,"intvolume":"       313","issue":"2","page":"405 - 424","_id":"2400","year":"2012","day":"01"}