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

Abstract

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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.

How to cite

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Lewin, 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 -

References

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