Stability and Absence of Binding for Multi-Polaron Systems

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 √ɑ, and with each other by Coulomb repulsion of strength U. We prove the following: (i)While there is a known thermodynamic instability for U < 2ɑ, stability of matter does hold for U > 2ɑ, 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 ɑ but not on N. The same results are shown to hold for the Pekar-Tomasevich model.

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