# Temperature dependence of condensate fraction of weakly nonideal trapped Bose gas

## Abstract

Condensation of the weakly nonideal gas in an anisotropic parabolic trap was considered. The first order (with respect to the interaction parameter) correction {Delta} n-bar{sub 0} = n-bar{sub 0}(T)-n-bar{sub 0}{sup 0}(T) to the temperature dependence of the ground state population n0-bar{sub 0}{sup 0}(T) of the ideal gas atoms was found using thermodynamic perturbation theory. The correction found n-bar{sub 0} proved to be much larger than the one calculated within the mean field theory [see Giorgini S, Pitaevskii L P, Stringari S Phys. Rev. A 54 R4633 (1996)] at temperatures below critical. This correction tends to zero as the temperature approaches the critical one; i.e., the interaction of the atoms does not lead to variation in the critical temperature. A simple analytic expression was found that describes the smooth variation of n-bar{sub 0}{sup 0}(T) as it approaches zero in the vicinity of the critical temperature. A new criterion for applicability of the thermodynamic limit is given. (laser applications and other topics in quantum electronics)

- Authors:

- P.N. Lebedev Physics Institute, Russian Academy of Sciences, Moscow (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21442711

- Resource Type:
- Journal Article

- Journal Name:
- Quantum Electronics (Woodbury, N.Y.)

- Additional Journal Information:
- Journal Volume: 30; Journal Issue: 5; Other Information: DOI: 10.1070/QE2000v030n05ABEH001738; Journal ID: ISSN 1063-7818

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; ATOMS; BOSE-EINSTEIN GAS; CONDENSATES; CORRECTIONS; CRITICAL TEMPERATURE; INTERACTIONS; MEAN-FIELD THEORY; PERTURBATION THEORY; TEMPERATURE DEPENDENCE; VARIATIONS; PHYSICAL PROPERTIES; THERMODYNAMIC PROPERTIES; TRANSITION TEMPERATURE

### Citation Formats

```
Alekseev, Vladimir A, and Krylova, Dar'ya D.
```*Temperature dependence of condensate fraction of weakly nonideal trapped Bose gas*. United States: N. p., 2000.
Web. doi:10.1070/QE2000V030N05ABEH001738.

```
Alekseev, Vladimir A, & Krylova, Dar'ya D.
```*Temperature dependence of condensate fraction of weakly nonideal trapped Bose gas*. United States. doi:10.1070/QE2000V030N05ABEH001738.

```
Alekseev, Vladimir A, and Krylova, Dar'ya D. Wed .
"Temperature dependence of condensate fraction of weakly nonideal trapped Bose gas". United States. doi:10.1070/QE2000V030N05ABEH001738.
```

```
@article{osti_21442711,
```

title = {Temperature dependence of condensate fraction of weakly nonideal trapped Bose gas},

author = {Alekseev, Vladimir A and Krylova, Dar'ya D},

abstractNote = {Condensation of the weakly nonideal gas in an anisotropic parabolic trap was considered. The first order (with respect to the interaction parameter) correction {Delta} n-bar{sub 0} = n-bar{sub 0}(T)-n-bar{sub 0}{sup 0}(T) to the temperature dependence of the ground state population n0-bar{sub 0}{sup 0}(T) of the ideal gas atoms was found using thermodynamic perturbation theory. The correction found n-bar{sub 0} proved to be much larger than the one calculated within the mean field theory [see Giorgini S, Pitaevskii L P, Stringari S Phys. Rev. A 54 R4633 (1996)] at temperatures below critical. This correction tends to zero as the temperature approaches the critical one; i.e., the interaction of the atoms does not lead to variation in the critical temperature. A simple analytic expression was found that describes the smooth variation of n-bar{sub 0}{sup 0}(T) as it approaches zero in the vicinity of the critical temperature. A new criterion for applicability of the thermodynamic limit is given. (laser applications and other topics in quantum electronics)},

doi = {10.1070/QE2000V030N05ABEH001738},

journal = {Quantum Electronics (Woodbury, N.Y.)},

issn = {1063-7818},

number = 5,

volume = 30,

place = {United States},

year = {2000},

month = {5}

}