Stability and absence of binding for multi-polaron systems
Frank, Rupert L.1 ; Lieb, Elliott H.2 ; Seiringer, Robert3 ; Thomas, Lawrence E.4
1 Department of Mathematics, Princeton University Washington Road, Princeton, NJ, 08544 USA
2 Departments of Mathematics and Physics, Princeton University P.O. Box 708, Princeton, NJ, 08544 USA
3 Department of Physics, Princeton University P.O. Box 708, Princeton, NJ, 08544 USA
4 Department of Mathematics, University of Virginia Charlottesville, VA, 22904 USA
Publications Mathématiques de l'IHÉS, Tome 113 (2011), pp. 39-67.

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.

DOI : 10.1007/s10240-011-0031-5
Frank, Rupert L. 1 ; Lieb, Elliott H. 2 ; Seiringer, Robert 3 ; Thomas, Lawrence E. 4

1 Department of Mathematics, Princeton University Washington Road, Princeton, NJ, 08544 USA
2 Departments of Mathematics and Physics, Princeton University P.O. Box 708, Princeton, NJ, 08544 USA
3 Department of Physics, Princeton University P.O. Box 708, Princeton, NJ, 08544 USA
4 Department of Mathematics, University of Virginia Charlottesville, VA, 22904 USA 
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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, Tome 113 (2011), pp. 39-67. doi : 10.1007/s10240-011-0031-5. http://archive.numdam.org/articles/10.1007/s10240-011-0031-5/

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