Binding, Stability, and Non-binding of Multi-polaron Systems

TL;DR

This paper investigates the conditions under which multi-polaron systems bind or remain unbound, establishing precise transition points, and discusses approximations and exact results for related models.

Contribution

It provides new theorems characterizing the transition from many-body collapse to thermodynamic limit and analyzes multi-polaron binding conditions.

Findings

Transition at U=2α for many-body collapse

No binding when U is sufficiently large

Exact results for a 1D toy model by Gross

Abstract

The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. 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. We also discuss the Pekar-Tomasevich approximation to the ground state energy, which is valid for large \alpha. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross.