Friday, February 24, 2012

1202.5103 (Mathieu Lewin et al.)

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

Mathieu Lewin, Nicolas Rougerie
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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