Ground state energy of large polaron systems

Journal Article · Sun Feb 15 00:00:00 EST 2015 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4908125· OSTI ID:22403095

Benguria, Rafael D., E-mail: [e-mail] ^[1]; Frank, Rupert L., E-mail: [e-mail] ^[2]; Lieb, Elliott H., E-mail: [e-mail] ^[3]

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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)

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}.

• OSTI ID: 22403095
• Journal Information: Journal of Mathematical Physics, Vol. 56, Issue 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
BOSONS
COULOMB FIELD
ELECTRONS
GROUND STATES