# Bose-Einstein condensation as a quantum phase transition in an optical lattice

Aizenman M, Lieb É, Seiringer R, Solovej J, Yngvason J. 2006.Bose-Einstein condensation as a quantum phase transition in an optical lattice. In: Mathematical Physics of Quantum Mechanics. LNP, vol. 690, 199–215.

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Author

Aizenman, Michael;
Lieb, Élliott H;
Seiringer, Robert

^{IST Austria}^{}; Solovej, Jan P; Yngvason, JakobBook Editor

Asch, Joachim;
Joye, Alain

Series Title

LNP

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.

Publishing Year

Date Published

2006-01-01

Book Title

Mathematical Physics of Quantum Mechanics

Volume

690

Page

199 - 215

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### Cite this

Aizenman M, Lieb É, Seiringer R, Solovej J, Yngvason J. Bose-Einstein condensation as a quantum phase transition in an optical lattice. In: Asch J, Joye A, eds.

*Mathematical Physics of Quantum Mechanics*. Vol 690. Springer; 2006:199-215. doi:10.1007/b11573432Aizenman, M., Lieb, É., Seiringer, R., Solovej, J., & Yngvason, J. (2006). Bose-Einstein condensation as a quantum phase transition in an optical lattice. In J. Asch & A. Joye (Eds.),

*Mathematical Physics of Quantum Mechanics*(Vol. 690, pp. 199–215). Springer. https://doi.org/10.1007/b11573432Aizenman, Michael, Élliott Lieb, Robert Seiringer, Jan Solovej, and Jakob Yngvason. “Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice.” In

*Mathematical Physics of Quantum Mechanics*, edited by Joachim Asch and Alain Joye, 690:199–215. Springer, 2006. https://doi.org/10.1007/b11573432.M. Aizenman, É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, “Bose-Einstein condensation as a quantum phase transition in an optical lattice,” in

*Mathematical Physics of Quantum Mechanics*, vol. 690, J. Asch and A. Joye, Eds. Springer, 2006, pp. 199–215.Aizenman, Michael, et al. “Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice.”

*Mathematical Physics of Quantum Mechanics*, edited by Joachim Asch and Alain Joye, vol. 690, Springer, 2006, pp. 199–215, doi:10.1007/b11573432.**All files available under the following license(s):**

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