On the binding of small polarons in a mean-field quantum crystal

Details On the binding of small polarons in a mean-field quantum crystal On the binding of small polarons in a mean-field quantum crystal

2012-02-23

arxiv.org/abs/1202.5103v1

Physics

Mathematical Physics

24 pages

Scientific paper

We consider a small multi-polaron model obtained by coupling the many-body Schr\"odinger equation for N interacting electrons with the energy functional of a mean- field crystal with a localized defect, obtaining a highly non linear many-body problem. The physical picture is that the electrons constitue a charge defect in an otherwise perfect periodic crystal. A remarkable feature of such a system is the possibility to form a bound state of electrons via their interaction with the polarizable background. We first prove that a single polaron always binds, i.e. the energy functional has a minimizer for N = 1. Then we discuss the case of multi-polarons containing two electrons or more. We show that their existence is guaranteed when certain quantized binding inequalities of HVZ type are satisfied.

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