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

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

2010-10-05

arxiv.org/abs/1010.0737v2

Physics

Condensed Matter

Strongly Correlated Electrons

12 pages; contribution to the proceedings of the conference QMath 11 (Hradec Kralove, September 2010); clarification added aft

Scientific paper

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.

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