Binding, Stability, and Non-binding of Multi-polaron Systems
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.
Cite
@article{arxiv.1010.0737,
title = {Binding, Stability, and Non-binding of Multi-polaron Systems},
author = {Rupert L. Frank and Elliott H. Lieb and Robert Seiringer and Lawrence E. Thomas},
journal= {arXiv preprint arXiv:1010.0737},
year = {2017}
}
Comments
12 pages; contribution to the proceedings of the conference QMath 11 (Hradec Kralove, September 2010); clarification added after Theorem 4.1