# Bose-Einstein-condensed systems in random potentials

## Abstract

The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles, and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state; but the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.

- Authors:

- Fachbereich Physik, Universitaet Duisburg-Essen, 47048 Duisburg (Germany)
- (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 20982170

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.023619; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; APPROXIMATIONS; BOSE-EINSTEIN CONDENSATION; COMPRESSIBILITY; CONDENSATES; DENSITY; GROUND STATES; INTERACTIONS; MEAN-FIELD THEORY; PHASE TRANSFORMATIONS; POTENTIALS; RANDOMNESS; SOUND WAVES; STABILITY; STOCHASTIC PROCESSES; STRUCTURE FACTORS; SUPERFLUIDITY; VELOCITY

### Citation Formats

```
Yukalov, V. I., Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, and Graham, R.
```*Bose-Einstein-condensed systems in random potentials*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.023619.

```
Yukalov, V. I., Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, & Graham, R.
```*Bose-Einstein-condensed systems in random potentials*. United States. doi:10.1103/PHYSREVA.75.023619.

```
Yukalov, V. I., Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, and Graham, R. Thu .
"Bose-Einstein-condensed systems in random potentials". United States.
doi:10.1103/PHYSREVA.75.023619.
```

```
@article{osti_20982170,
```

title = {Bose-Einstein-condensed systems in random potentials},

author = {Yukalov, V. I. and Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980 and Graham, R.},

abstractNote = {The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles, and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state; but the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.},

doi = {10.1103/PHYSREVA.75.023619},

journal = {Physical Review. A},

number = 2,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}