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

Mathieu Lewin (1) , Nicolas Rougerie (2)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 LPM2C - Laboratoire de physique et modélisation des milieux condensés

We consider a small multi-polaron model obtained by coupling the many-body Schrödinger 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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Mathieu Lewin, Nicolas Rougerie. On the binding of small polarons in a mean-field quantum crystal. 2012. ⟨hal-00673045v1⟩