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. Fr\"ohlich'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<2\alpha, stability of matter does hold for U>2\alpha, 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 \alpha but not on N. The same results are shown to hold for the Pekar-Tomasevich model.