@inbook{5919d7bea2134298ac76d993e505bef3,

title = "Bose-Einstein condensation as a quantum phase transition in an optical lattice",

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.",

author = "M. Aizenman and Lieb, {E. H.} and R. Seiringer and Solovej, {J. P.} and J. Yngvason",

year = "2006",

doi = "10.1007/3-540-34273-7_16",

language = "English (US)",

isbn = "3540310266",

series = "Lecture Notes in Physics",

pages = "199--215",

editor = "Joachim Asch and Alain Joye",

booktitle = "Mathematical Physics of Quantum Mechanics",

}