# 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:

- Instituto de Física, Pontificia Universidad Católica de Chile, Santiago (Chile)
- Mathematics 253-37, Caltech, Pasadena, California 91125 (United States)
- 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}

}

DOI: 10.1063/1.4908125

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