### Abstract

One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state composed of localized atoms as the strength of a periodic, optical trapping potential is varied. In [1] a model of this phenomenon has been analyzed rigorously. The gas is a hard core lattice gas and the optical lattice is modeled by a periodic potential of strength λ. For small λ and temperature Bose- Einstein condensation (BEC) is proved to occur, while at large λ BEC disappears, even in the ground state, which is a Mott-insulator state with a characteristic gap. The inter-particle interaction is essential for this effect. This contribution gives a pedagogical survey of these results.

Original language | English (US) |
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Title of host publication | Mathematical Physics of Quantum Mechanics |

Subtitle of host publication | Selected and Refereed Lectures from QMath9 |

Editors | Joachim Asch, Alain Joye |

Pages | 199-215 |

Number of pages | 17 |

DOIs | |

State | Published - 2006 |

### Publication series

Name | Lecture Notes in Physics |
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Volume | 690 |

ISSN (Print) | 0075-8450 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

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## Cite this

*Mathematical Physics of Quantum Mechanics: Selected and Refereed Lectures from QMath9*(pp. 199-215). (Lecture Notes in Physics; Vol. 690). https://doi.org/10.1007/3-540-34273-7_16