On the binding of polarons in a mean-field quantum crystal
ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 3, p. 629-656

We consider a 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 constitute 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 prove first 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 N ≥ 2 electrons. We show that their existence is guaranteed when certain quantized binding inequalities of HVZ type are satisfied.

DOI : https://doi.org/10.1051/cocv/2012025
Classification:  35Q40,  49J40
Keywords: polaron, quantum crystal, binding inequalities, hvz theorem, choquard-pekar equation
@article{COCV_2013__19_3_629_0,
     author = {Lewin, Mathieu and Rougerie, Nicolas},
     title = {On the binding of polarons in a mean-field quantum crystal},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {3},
     year = {2013},
     pages = {629-656},
     doi = {10.1051/cocv/2012025},
     zbl = {1291.35248},
     mrnumber = {3092354},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2013__19_3_629_0}
}
Lewin, Mathieu; Rougerie, Nicolas. On the binding of polarons in a mean-field quantum crystal. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 3, pp. 629-656. doi : 10.1051/cocv/2012025. http://www.numdam.org/item/COCV_2013__19_3_629_0/

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