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Stability and Absence of Binding for Multi-Polaron Systems

We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N\geq 2 polarons. Fröhlich&#39;s 1937 polaron model describes non-relativistic particles interacting with a scalar quantized field with coupling \sqrtα, 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\to\infty. (ii) There is no binding of any kind if U exceeds a critical value that depends on αbut not on N. The same results are shown to hold for the Pekar-Tomasevich model.