# Vortex distribution in the lowest Landau level

## Abstract

We study the vortex distribution of the wave functions minimizing the Gross-Pitaevskii energy for a fast rotating condensate in the lowest Landau level (LLL): we prove that the minimizer cannot have a finite number of zeroes, thus the lattice is infinite, but not uniform. This uses the explicit expression of the projector onto the LLL. We also show that any slow varying envelope function can be approximated in the LLL by distorting the lattice. This is used in particular to approximate the inverted parabola and understand the role of 'invisible' vortices: the distortion of the lattice is very small in the Thomas-Fermi region but quite large outside, where the 'invisible' vortices lie.

- Authors:

- Laboratoire Jacques-Louis Lions, UMR-CNRS 7598, Universite Paris 6, 175 rue du Chevaleret, 75013 Paris (France)
- (France)

- Publication Date:

- OSTI Identifier:
- 20786627

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 73; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.73.011601; (c) 2006 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; DISTRIBUTION; ENERGY LEVELS; THOMAS-FERMI MODEL; VORTICES; WAVE EQUATIONS; WAVE FUNCTIONS

### Citation Formats

```
Aftalion, Amandine, Blanc, Xavier, Nier, Francis, and IRMAR, UMR-CNRS 6625, Universite Rennes 1, 35042 Rennes Cedex.
```*Vortex distribution in the lowest Landau level*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVA.73.0.

```
Aftalion, Amandine, Blanc, Xavier, Nier, Francis, & IRMAR, UMR-CNRS 6625, Universite Rennes 1, 35042 Rennes Cedex.
```*Vortex distribution in the lowest Landau level*. United States. doi:10.1103/PHYSREVA.73.0.

```
Aftalion, Amandine, Blanc, Xavier, Nier, Francis, and IRMAR, UMR-CNRS 6625, Universite Rennes 1, 35042 Rennes Cedex. Sun .
"Vortex distribution in the lowest Landau level". United States.
doi:10.1103/PHYSREVA.73.0.
```

```
@article{osti_20786627,
```

title = {Vortex distribution in the lowest Landau level},

author = {Aftalion, Amandine and Blanc, Xavier and Nier, Francis and IRMAR, UMR-CNRS 6625, Universite Rennes 1, 35042 Rennes Cedex},

abstractNote = {We study the vortex distribution of the wave functions minimizing the Gross-Pitaevskii energy for a fast rotating condensate in the lowest Landau level (LLL): we prove that the minimizer cannot have a finite number of zeroes, thus the lattice is infinite, but not uniform. This uses the explicit expression of the projector onto the LLL. We also show that any slow varying envelope function can be approximated in the LLL by distorting the lattice. This is used in particular to approximate the inverted parabola and understand the role of 'invisible' vortices: the distortion of the lattice is very small in the Thomas-Fermi region but quite large outside, where the 'invisible' vortices lie.},

doi = {10.1103/PHYSREVA.73.0},

journal = {Physical Review. A},

number = 1,

volume = 73,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}

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