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1 results

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

  • Mathieu Lewin, Nicolas Rougerie
  • Journal:
    ESAIM: Control, Optimisation and Calculus of Variations / Volume 19 / Issue 3 / July 2013
    Published online by Cambridge University Press:
    28 March 2013, pp. 629-656
    Print publication:
    July 2013

  • We consider a multi-polaron model obtained by coupling the many-body Schrödinger equationfor N interacting electrons with the energy functional of a mean-fieldcrystal with a localized defect, obtaining a highly non linear many-body problem. Thephysical picture is that the electrons constitute a charge defect in an otherwise perfectperiodic crystal. A remarkable feature of such a system is the possibility to form a boundstate of electrons via their interaction with the polarizable background. We prove firstthat a single polaron always binds, i.e. the energy functional has aminimizer for N = 1. Then we discuss the case of multi-polaronscontaining N ≥ 2 electrons. We show that their existence is guaranteedwhen certain quantized binding inequalities of HVZ type are satisfied.