Stability and absence of binding for multi-polaron systems

We prove two facts about the binding of polarons, or its absence, which have been longstanding problems. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at $U = 2\alpha$, where $U$ is the electronic Coulomb repulsion and $\alpha$ is the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. While these results are valid for quantized fields (the Froehlich model), in the talk we will focus on the technically easier case of classical fields (the Pekar-Tomasevich model).

(The talk is based on joint work with E. H. Lieb, R. Seiringer and L. E. Thomas.)