{"page":"199 - 215","editor":[{"first_name":"Joachim","last_name":"Asch","full_name":"Asch, Joachim"},{"first_name":"Alain","last_name":"Joye","full_name":"Joye, Alain"}],"extern":1,"status":"public","intvolume":"       690","quality_controlled":0,"publisher":"Springer","publist_id":"4559","year":"2006","oa":1,"abstract":[{"lang":"eng","text":"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."}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/cond-mat/0412034"}],"title":"Bose-Einstein condensation as a quantum phase transition in an optical lattice","doi":"10.1007/b11573432","date_updated":"2021-01-12T06:57:04Z","month":"01","author":[{"first_name":"Michael","full_name":"Aizenman, Michael","last_name":"Aizenman"},{"full_name":"Lieb, Élliott H","last_name":"Lieb","first_name":"Élliott"},{"first_name":"Robert","full_name":"Robert Seiringer","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"},{"first_name":"Jan","full_name":"Solovej, Jan P","last_name":"Solovej"},{"last_name":"Yngvason","full_name":"Yngvason, Jakob","first_name":"Jakob"}],"volume":690,"_id":"2369","alternative_title":["LNP"],"date_published":"2006-01-01T00:00:00Z","publication":"Mathematical Physics of Quantum Mechanics","publication_status":"published","date_created":"2018-12-11T11:57:16Z","day":"01","citation":{"mla":"Aizenman, Michael, et al. “Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice.” <i>Mathematical Physics of Quantum Mechanics</i>, edited by Joachim Asch and Alain Joye, vol. 690, Springer, 2006, pp. 199–215, doi:<a href=\"https://doi.org/10.1007/b11573432\">10.1007/b11573432</a>.","ista":"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.","short":"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.","ama":"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. <i>Mathematical Physics of Quantum Mechanics</i>. Vol 690. Springer; 2006:199-215. doi:<a href=\"https://doi.org/10.1007/b11573432\">10.1007/b11573432</a>","ieee":"M. Aizenman, É. Lieb, R. Seiringer, J. Solovej, and J. Yngvason, “Bose-Einstein condensation as a quantum phase transition in an optical lattice,” in <i>Mathematical Physics of Quantum Mechanics</i>, vol. 690, J. Asch and A. Joye, Eds. Springer, 2006, pp. 199–215.","apa":"Aizenman, M., Lieb, É., Seiringer, R., Solovej, J., &#38; Yngvason, J. (2006). Bose-Einstein condensation as a quantum phase transition in an optical lattice. In J. Asch &#38; A. Joye (Eds.), <i>Mathematical Physics of Quantum Mechanics</i> (Vol. 690, pp. 199–215). Springer. <a href=\"https://doi.org/10.1007/b11573432\">https://doi.org/10.1007/b11573432</a>","chicago":"Aizenman, Michael, Élliott Lieb, Robert Seiringer, Jan Solovej, and Jakob Yngvason. “Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice.” In <i>Mathematical Physics of Quantum Mechanics</i>, edited by Joachim Asch and Alain Joye, 690:199–215. Springer, 2006. <a href=\"https://doi.org/10.1007/b11573432\">https://doi.org/10.1007/b11573432</a>."},"type":"book_chapter"}