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 $\sqrt{\alpha}$, and with each other by Coulomb repulsion of strength U. We prove the following: (i) While there is a known thermodynamic instability for U<2α, stability of matter does hold for U>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.
@article{PMIHES_2011__113__39_0, author = {Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert and Thomas, Lawrence E.}, title = {Stability and absence of binding for~multi-polaron systems}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {39--67}, publisher = {Springer-Verlag}, volume = {113}, year = {2011}, doi = {10.1007/s10240-011-0031-5}, mrnumber = {2805597}, zbl = {1227.82083}, language = {en}, url = {http://www.numdam.org/articles/10.1007/s10240-011-0031-5/} }
TY - JOUR AU - Frank, Rupert L. AU - Lieb, Elliott H. AU - Seiringer, Robert AU - Thomas, Lawrence E. TI - Stability and absence of binding for multi-polaron systems JO - Publications Mathématiques de l'IHÉS PY - 2011 SP - 39 EP - 67 VL - 113 PB - Springer-Verlag UR - http://www.numdam.org/articles/10.1007/s10240-011-0031-5/ DO - 10.1007/s10240-011-0031-5 LA - en ID - PMIHES_2011__113__39_0 ER -
%0 Journal Article %A Frank, Rupert L. %A Lieb, Elliott H. %A Seiringer, Robert %A Thomas, Lawrence E. %T Stability and absence of binding for multi-polaron systems %J Publications Mathématiques de l'IHÉS %D 2011 %P 39-67 %V 113 %I Springer-Verlag %U http://www.numdam.org/articles/10.1007/s10240-011-0031-5/ %R 10.1007/s10240-011-0031-5 %G en %F PMIHES_2011__113__39_0
Frank, Rupert L.; Lieb, Elliott H.; Seiringer, Robert; Thomas, Lawrence E. Stability and absence of binding for multi-polaron systems. Publications Mathématiques de l'IHÉS, Volume 113 (2011), pp. 39-67. doi : 10.1007/s10240-011-0031-5. http://www.numdam.org/articles/10.1007/s10240-011-0031-5/
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