Abstract
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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Frank, R.L., Lieb, E.H., Seiringer, R. et al. Stability and absence of binding for multi-polaron systems. Publ.math.IHES 113, 39–67 (2011). https://doi.org/10.1007/s10240-011-0031-5
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DOI: https://doi.org/10.1007/s10240-011-0031-5