# Semiclassical corrections to a static Bose-Einstein condensate at zero temperature

## Abstract

In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensate or, equivalently, by the hydrodynamic equations for the number density and current density. These equations receive corrections from quantum field fluctuations around the mean field. We calculate the semiclassical corrections to these equations for a general time-independent state of the condensate, extending previous work to include vortex states as well as the ground state. In the Thomas-Fermi limit, the semiclassical corrections can be taken into account by adding a local correction term to the Gross-Pitaevskii equation. At second order in the Thomas-Fermi expansion, the semiclassical corrections can be taken into account by adding local correction terms to the hydrodynamic equations. [copyright] [ital 1999] [ital The American Physical Society]

- Authors:

- (Department of Physics, The Ohio State University, Columbus, Ohio 43210 (United States))

- Publication Date:

- OSTI Identifier:
- 6468658

- Alternate Identifier(s):
- OSTI ID: 6468658

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review A

- Additional Journal Information:
- Journal Volume: 60:3; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BOSE-EINSTEIN CONDENSATION; CORRECTIONS; FLUCTUATIONS; SEMICLASSICAL APPROXIMATION; TEMPERATURE ZERO K; THOMAS-FERMI MODEL; ATOMIC MODELS; MATHEMATICAL MODELS; VARIATIONS 665400* -- Quantum Physics Aspects of Condensed Matter-- (1992-)

### Citation Formats

```
Andersen, J.O., and Braaten, E.
```*Semiclassical corrections to a static Bose-Einstein condensate at zero temperature*. United States: N. p., 1999.
Web. doi:10.1103/PhysRevA.60.2330.

```
Andersen, J.O., & Braaten, E.
```*Semiclassical corrections to a static Bose-Einstein condensate at zero temperature*. United States. doi:10.1103/PhysRevA.60.2330.

```
Andersen, J.O., and Braaten, E. Wed .
"Semiclassical corrections to a static Bose-Einstein condensate at zero temperature". United States. doi:10.1103/PhysRevA.60.2330.
```

```
@article{osti_6468658,
```

title = {Semiclassical corrections to a static Bose-Einstein condensate at zero temperature},

author = {Andersen, J.O. and Braaten, E.},

abstractNote = {In the mean-field approximation, a trapped Bose-Einstein condensate at zero temperature is described by the Gross-Pitaevskii equation for the condensate or, equivalently, by the hydrodynamic equations for the number density and current density. These equations receive corrections from quantum field fluctuations around the mean field. We calculate the semiclassical corrections to these equations for a general time-independent state of the condensate, extending previous work to include vortex states as well as the ground state. In the Thomas-Fermi limit, the semiclassical corrections can be taken into account by adding a local correction term to the Gross-Pitaevskii equation. At second order in the Thomas-Fermi expansion, the semiclassical corrections can be taken into account by adding local correction terms to the hydrodynamic equations. [copyright] [ital 1999] [ital The American Physical Society]},

doi = {10.1103/PhysRevA.60.2330},

journal = {Physical Review A},

issn = {1050-2947},

number = ,

volume = 60:3,

place = {United States},

year = {1999},

month = {9}

}