Ground state energy of large polaron systems

Rafael D. Benguria; Rupert L. Frank; Elliott H. Lieb

doi:10.1063/1.4908125

Ground state energy of large polaron systems

Rafael D. Benguria
, Rupert L. Frank
, Elliott H. Lieb

Mathematics

Research output: Contribution to journal › Article › peer-review

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^7/5, and we give upper and lower bounds on the asymptotic coefficient that agree to within a factor of 2^2/5.

Original language	English (US)
Article number	021901
Journal	Journal of Mathematical Physics
Volume	56
Issue number	2
DOIs	https://doi.org/10.1063/1.4908125
State	Published - Feb 18 2015

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.4908125

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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 -N7/5, and we give upper and lower bounds on the asymptotic coefficient that agree to within a factor of 22/5.",

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AU - Lieb, Elliott H.

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N2 - 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 -N7/5, and we give upper and lower bounds on the asymptotic coefficient that agree to within a factor of 22/5.

AB - 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 -N7/5, and we give upper and lower bounds on the asymptotic coefficient that agree to within a factor of 22/5.

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Ground state energy of large polaron systems

Abstract

All Science Journal Classification (ASJC) codes

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