# Heidelberg 2015 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 15: Poster: Quantum Optics and Photonics I

### Q 15.34: Poster

### Montag, 23. März 2015, 17:00–19:00, C/Foyer

**Failure of extended mean-field theories in one-dimensional Bose gases** — Tim Sauer and •Carsten Henkel — University of Potsdam, Germany

Due to large thermal fluctuations, low-dimensional Bose gases do not develop a proper condensate, and even the onset of quasi-condensation turns into a cross-over rather than a phase transition. This is actually a challenge to reproduce within a mean-field theory because the modeling of the system seems to require a larger number of relevant hydrodynamic fields. In other words, the statistics of the quantum field is far from Gaussian in the cross-over region. We outline a zoology of mean-field theories [1,2] and develop efficient analytical formulas using a high-temperature expansion. The problems of the theories are illustrated by studying the equation of state and density fluctuations.

[1]
C. Mora and Y. Castin,
*Phys. Rev. A* **67** (2003) 053615.

[2]
R. Walser,
*Opt. Commun.* **243** (2004) 107