# Bose-Einstein condensation on a manifold with non-negative Ricci curvature

## Abstract

The Bose-Einstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with non-negative Ricci curvature is investigated using the heat kernel and eigenvalue estimates of the Laplace operator. The main focus is on the nonrelativistic gas. However, special relativistic ideal gas is also discussed. The thermodynamic limit of the heat kernel and eigenvalue estimates is taken and the results are used to derive bounds for the depletion coefficient. In the case of a weakly interacting gas, Bogoliubov approximation is employed. The ground state is analyzed using heat kernel methods and finite size effects on the ground state energy are proposed. The justification of the c-number substitution on a manifold is given.

- Authors:

- Department of Physics, Boğaziçi University, 34342 Bebek, Istanbul (Turkey)

- Publication Date:

- OSTI Identifier:
- 22403091

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 1; 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; BOSE-EINSTEIN CONDENSATION; BOSE-EINSTEIN GAS; EIGENVALUES; GROUND STATES; HEAT; KERNELS; LAPLACIAN

### Citation Formats

```
Akant, Levent, E-mail: levent.akant@boun.edu.tr, Ertuğrul, Emine, E-mail: emine.ertugrul@boun.edu.tr, Tapramaz, Ferzan, E-mail: waskhez@gmail.com, and Turgut, O. Teoman, E-mail: turgutte@boun.edu.tr.
```*Bose-Einstein condensation on a manifold with non-negative Ricci curvature*. United States: N. p., 2015.
Web. doi:10.1063/1.4906135.

```
Akant, Levent, E-mail: levent.akant@boun.edu.tr, Ertuğrul, Emine, E-mail: emine.ertugrul@boun.edu.tr, Tapramaz, Ferzan, E-mail: waskhez@gmail.com, & Turgut, O. Teoman, E-mail: turgutte@boun.edu.tr.
```*Bose-Einstein condensation on a manifold with non-negative Ricci curvature*. United States. doi:10.1063/1.4906135.

```
Akant, Levent, E-mail: levent.akant@boun.edu.tr, Ertuğrul, Emine, E-mail: emine.ertugrul@boun.edu.tr, Tapramaz, Ferzan, E-mail: waskhez@gmail.com, and Turgut, O. Teoman, E-mail: turgutte@boun.edu.tr. Thu .
"Bose-Einstein condensation on a manifold with non-negative Ricci curvature". United States.
doi:10.1063/1.4906135.
```

```
@article{osti_22403091,
```

title = {Bose-Einstein condensation on a manifold with non-negative Ricci curvature},

author = {Akant, Levent, E-mail: levent.akant@boun.edu.tr and Ertuğrul, Emine, E-mail: emine.ertugrul@boun.edu.tr and Tapramaz, Ferzan, E-mail: waskhez@gmail.com and Turgut, O. Teoman, E-mail: turgutte@boun.edu.tr},

abstractNote = {The Bose-Einstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with non-negative Ricci curvature is investigated using the heat kernel and eigenvalue estimates of the Laplace operator. The main focus is on the nonrelativistic gas. However, special relativistic ideal gas is also discussed. The thermodynamic limit of the heat kernel and eigenvalue estimates is taken and the results are used to derive bounds for the depletion coefficient. In the case of a weakly interacting gas, Bogoliubov approximation is employed. The ground state is analyzed using heat kernel methods and finite size effects on the ground state energy are proposed. The justification of the c-number substitution on a manifold is given.},

doi = {10.1063/1.4906135},

journal = {Journal of Mathematical Physics},

number = 1,

volume = 56,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}