# Virial theorems for vortex states in a confined Bose-Einstein condensate

## Abstract

We derive a class of virial theorems which provide stringent tests of both analytical and numerical calculations of vortex states in a confined Bose-Einstein condensate. In the special case of harmonic confinement we arrive at the somewhat surprising conclusion that the linear moments of the particle density, as well as the linear momentum, must vanish even in the presence of off-center vortices which lack axial or reflection symmetry. Illustrations are provided by some analytical results in the limit of a dilute gas, and by a numerical calculation of a class of single and double vortices at intermediate couplings. The effect of anharmonic confinement is also discussed.

- Authors:

- Department of Physics, University of Crete, and Research Center of Crete, Heraklion (Greece)
- (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 20786555

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.72.053609; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; BOSE-EINSTEIN CONDENSATION; CONFINEMENT; DENSITY; LINEAR MOMENTUM; REFLECTION; SYMMETRY; VIRIAL THEOREM; VORTICES

### Citation Formats

```
Papanicolaou, N., Komineas, S., Cooper, N. R., and Theory of Condensed Matter Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE.
```*Virial theorems for vortex states in a confined Bose-Einstein condensate*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Papanicolaou, N., Komineas, S., Cooper, N. R., & Theory of Condensed Matter Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE.
```*Virial theorems for vortex states in a confined Bose-Einstein condensate*. United States. doi:10.1103/PHYSREVA.72.0.

```
Papanicolaou, N., Komineas, S., Cooper, N. R., and Theory of Condensed Matter Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE. Tue .
"Virial theorems for vortex states in a confined Bose-Einstein condensate". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786555,
```

title = {Virial theorems for vortex states in a confined Bose-Einstein condensate},

author = {Papanicolaou, N. and Komineas, S. and Cooper, N. R. and Theory of Condensed Matter Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE},

abstractNote = {We derive a class of virial theorems which provide stringent tests of both analytical and numerical calculations of vortex states in a confined Bose-Einstein condensate. In the special case of harmonic confinement we arrive at the somewhat surprising conclusion that the linear moments of the particle density, as well as the linear momentum, must vanish even in the presence of off-center vortices which lack axial or reflection symmetry. Illustrations are provided by some analytical results in the limit of a dilute gas, and by a numerical calculation of a class of single and double vortices at intermediate couplings. The effect of anharmonic confinement is also discussed.},

doi = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 5,

volume = 72,

place = {United States},

year = {Tue Nov 15 00:00:00 EST 2005},

month = {Tue Nov 15 00:00:00 EST 2005}

}

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