{"volume":113,"publisher":"Springer","publication":"Publications Mathematiques de l Institut des Hautes Etudes Scientifiques","_id":"2390","status":"public","type":"journal_article","publication_status":"published","day":"01","quality_controlled":0,"date_updated":"2021-01-12T06:57:12Z","page":"39 - 67","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1004.4892"}],"year":"2011","issue":"1","extern":1,"intvolume":"       113","title":"Stability and absence of binding for multi-polaron systems","month":"06","author":[{"last_name":"Frank","full_name":"Frank, Rupert L","first_name":"Rupert"},{"last_name":"Lieb","full_name":"Lieb, Élliott H","first_name":"Élliott"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer"},{"first_name":"Lawrence","last_name":"Thomas","full_name":"Thomas, Lawrence E"}],"date_created":"2018-12-11T11:57:23Z","publist_id":"4534","doi":"10.1007/s10240-011-0031-5","abstract":[{"text":"We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N≥2 polarons. Fröhlich's 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling √α, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U&lt;2α, stability of matter does hold for U&gt;2α, that is, the ground state energy per particle has a finite limit as N→∞. (ii) There is no binding of any kind if U exceeds a critical value that depends on α but not on N. The same results are shown to hold for the Pekar-Tomasevich model.","lang":"eng"}],"date_published":"2011-06-01T00:00:00Z","citation":{"ista":"Frank R, Lieb É, Seiringer R, Thomas L. 2011. Stability and absence of binding for multi-polaron systems. Publications Mathematiques de l Institut des Hautes Etudes Scientifiques. 113(1), 39–67.","ieee":"R. Frank, É. Lieb, R. Seiringer, and L. Thomas, “Stability and absence of binding for multi-polaron systems,” <i>Publications Mathematiques de l Institut des Hautes Etudes Scientifiques</i>, vol. 113, no. 1. Springer, pp. 39–67, 2011.","chicago":"Frank, Rupert, Élliott Lieb, Robert Seiringer, and Lawrence Thomas. “Stability and Absence of Binding for Multi-Polaron Systems.” <i>Publications Mathematiques de l Institut Des Hautes Etudes Scientifiques</i>. Springer, 2011. <a href=\"https://doi.org/10.1007/s10240-011-0031-5\">https://doi.org/10.1007/s10240-011-0031-5</a>.","mla":"Frank, Rupert, et al. “Stability and Absence of Binding for Multi-Polaron Systems.” <i>Publications Mathematiques de l Institut Des Hautes Etudes Scientifiques</i>, vol. 113, no. 1, Springer, 2011, pp. 39–67, doi:<a href=\"https://doi.org/10.1007/s10240-011-0031-5\">10.1007/s10240-011-0031-5</a>.","short":"R. Frank, É. Lieb, R. Seiringer, L. Thomas, Publications Mathematiques de l Institut Des Hautes Etudes Scientifiques 113 (2011) 39–67.","ama":"Frank R, Lieb É, Seiringer R, Thomas L. Stability and absence of binding for multi-polaron systems. <i>Publications Mathematiques de l Institut des Hautes Etudes Scientifiques</i>. 2011;113(1):39-67. doi:<a href=\"https://doi.org/10.1007/s10240-011-0031-5\">10.1007/s10240-011-0031-5</a>","apa":"Frank, R., Lieb, É., Seiringer, R., &#38; Thomas, L. (2011). Stability and absence of binding for multi-polaron systems. <i>Publications Mathematiques de l Institut Des Hautes Etudes Scientifiques</i>. Springer. <a href=\"https://doi.org/10.1007/s10240-011-0031-5\">https://doi.org/10.1007/s10240-011-0031-5</a>"}}