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Title: Ground state energy of large polaron systems

Abstract

The last unsolved problem about the many-polaron system, in the Pekar–Tomasevich approximation, is the case of bosons with the electron-electron Coulomb repulsion of strength exactly 1 (the “neutral case”). We prove that the ground state energy, for large N, goes exactly as −N{sup 7/5}, and we give upper and lower bounds on the asymptotic coefficient that agree to within a factor of 2{sup 2/5}.

Authors:
 [1];  [2];  [3]
  1. Instituto de Física, Pontificia Universidad Católica de Chile, Santiago (Chile)
  2. Mathematics 253-37, Caltech, Pasadena, California 91125 (United States)
  3. Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey 08544 (United States)
Publication Date:
OSTI Identifier:
22403095
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; ASYMPTOTIC SOLUTIONS; BOSONS; COULOMB FIELD; ELECTRONS; GROUND STATES

Citation Formats

Benguria, Rafael D., E-mail: rbenguri@fis.puc.cl, Frank, Rupert L., E-mail: rlfrank@caltech.edu, and Lieb, Elliott H., E-mail: lieb@princeton.edu. Ground state energy of large polaron systems. United States: N. p., 2015. Web. doi:10.1063/1.4908125.
Benguria, Rafael D., E-mail: rbenguri@fis.puc.cl, Frank, Rupert L., E-mail: rlfrank@caltech.edu, & Lieb, Elliott H., E-mail: lieb@princeton.edu. Ground state energy of large polaron systems. United States. doi:10.1063/1.4908125.
Benguria, Rafael D., E-mail: rbenguri@fis.puc.cl, Frank, Rupert L., E-mail: rlfrank@caltech.edu, and Lieb, Elliott H., E-mail: lieb@princeton.edu. Sun . "Ground state energy of large polaron systems". United States. doi:10.1063/1.4908125.
@article{osti_22403095,
title = {Ground state energy of large polaron systems},
author = {Benguria, Rafael D., E-mail: rbenguri@fis.puc.cl and Frank, Rupert L., E-mail: rlfrank@caltech.edu and Lieb, Elliott H., E-mail: lieb@princeton.edu},
abstractNote = {The last unsolved problem about the many-polaron system, in the Pekar–Tomasevich approximation, is the case of bosons with the electron-electron Coulomb repulsion of strength exactly 1 (the “neutral case”). We prove that the ground state energy, for large N, goes exactly as −N{sup 7/5}, and we give upper and lower bounds on the asymptotic coefficient that agree to within a factor of 2{sup 2/5}.},
doi = {10.1063/1.4908125},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 56,
place = {United States},
year = {Sun Feb 15 00:00:00 EST 2015},
month = {Sun Feb 15 00:00:00 EST 2015}
}