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Stability and absence of binding for multi-polaron systems
Rupert L. Frank1 ; Elliott H. Lieb2 ; Robert Seiringer3 ; Lawrence E. Thomas4
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, Volume 113 (2011), pp. 39-67
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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.

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DOI: 10.1007/s10240-011-0031-5

Rupert L. Frank 1; Elliott H. Lieb 2; Robert Seiringer 3; Lawrence E. Thomas 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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Rupert L. Frank; Elliott H. Lieb; Robert Seiringer; Lawrence E. Thomas. 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

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