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

Mathieu Lewin; Nicolas Rougerie

ESAIM: Control, Optimisation and Calculus of Variations (2013)

- Volume: 19, Issue: 3, page 629-656
- ISSN: 1292-8119

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topLewin, Mathieu, and Rougerie, Nicolas. "On the binding of polarons in a mean-field quantum crystal." ESAIM: Control, Optimisation and Calculus of Variations 19.3 (2013): 629-656. <http://eudml.org/doc/272948>.

@article{Lewin2013,

abstract = {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.},

author = {Lewin, Mathieu, Rougerie, Nicolas},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {polaron; quantum crystal; binding inequalities; hvz theorem; choquard-pekar equation; HVZ theorem; Choquard-pekar equation},

language = {eng},

number = {3},

pages = {629-656},

publisher = {EDP-Sciences},

title = {On the binding of polarons in a mean-field quantum crystal},

url = {http://eudml.org/doc/272948},

volume = {19},

year = {2013},

}

TY - JOUR

AU - Lewin, Mathieu

AU - Rougerie, Nicolas

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

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2013

PB - EDP-Sciences

VL - 19

IS - 3

SP - 629

EP - 656

AB - 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.

LA - eng

KW - polaron; quantum crystal; binding inequalities; hvz theorem; choquard-pekar equation; HVZ theorem; Choquard-pekar equation

UR - http://eudml.org/doc/272948

ER -

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