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

M. Aizenman, É. Lieb, R. Seiringer, J. Solovej, J. Yngvason, in:, J. Asch, A. Joye (Eds.), Mathematical Physics of Quantum Mechanics, Springer, 2006, pp. 199–215.


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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/b11573432
Aizenman, 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/b11573432
Aizenman, 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 M, Lieb É, Seiringer R, Solovej J, Yngvason J. 2006. Bose-Einstein condensation as a quantum phase transition in an optical lattice. Mathematical Physics of Quantum Mechanics. , LNP, vol. 690. 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.

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