[{"intvolume":" 4713","extern":1,"status":"public","alternative_title":["LNCS"],"publist_id":"2656","date_updated":"2021-01-12T07:51:35Z","author":[{"full_name":"Ulges, Adrian","last_name":"Ulges","first_name":"Adrian"},{"first_name":"Christoph","orcid":"0000-0001-8622-7887","id":"40C20FD2-F248-11E8-B48F-1D18A9856A87","last_name":"Lampert","full_name":"Christoph Lampert"},{"first_name":"Daniel","last_name":"Keysers","full_name":"Keysers,Daniel"},{"full_name":"Breuel,Thomas M","last_name":"Breuel","first_name":"Thomas"}],"type":"conference","volume":4713,"date_created":"2018-12-11T12:04:42Z","publication_status":"published","year":"2007","month":"11","_id":"3701","date_published":"2007-11-09T00:00:00Z","page":"204 - 213","quality_controlled":0,"abstract":[{"lang":"eng","text":"The extraction of a parametric global motion from a motion field is a task with several applications in video processing. We present two probabilistic formulations of the problem and carry out optimization using the RAST algorithm, a geometric matching method novel to motion estimation in video. RAST uses an exhaustive and adaptive search of transformation space and thus gives – in contrast to local sampling optimization techniques used in the past – a globally optimal solution. Among other applications, our framework can thus be used as a source of ground truth for benchmarking motion estimation algorithms.\n\nOur main contributions are: first, the novel combination of a state-of-the-art MAP criterion for dominant motion estimation with a search procedure that guarantees global optimality. Second, experimental results that illustrate the superior performance of our approach on synthetic flow fields as well as real-world video streams. Third, a significant speedup of the search achieved by extending the model with an additional smoothness prior."}],"title":"Optimal dominant motion estimation using adaptive search of transformation space","publisher":"Springer","citation":{"ista":"Ulges A, Lampert C, Keysers D, Breuel T. 2007. Optimal dominant motion estimation using adaptive search of transformation space. DAGM: German Association For Pattern Recognition, LNCS, vol. 4713, 204–213.","ieee":"A. Ulges, C. Lampert, D. Keysers, and T. Breuel, “Optimal dominant motion estimation using adaptive search of transformation space,” presented at the DAGM: German Association For Pattern Recognition, 2007, vol. 4713, pp. 204–213.","mla":"Ulges, Adrian, et al. *Optimal Dominant Motion Estimation Using Adaptive Search of Transformation Space*. Vol. 4713, Springer, 2007, pp. 204–13, doi:10.1007/978-3-540-74936-3_21.","short":"A. Ulges, C. Lampert, D. Keysers, T. Breuel, in:, Springer, 2007, pp. 204–213.","apa":"Ulges, A., Lampert, C., Keysers, D., & Breuel, T. (2007). Optimal dominant motion estimation using adaptive search of transformation space (Vol. 4713, pp. 204–213). Presented at the DAGM: German Association For Pattern Recognition, Springer. https://doi.org/10.1007/978-3-540-74936-3_21","chicago":"Ulges, Adrian, Christoph Lampert, Daniel Keysers, and Thomas Breuel. “Optimal Dominant Motion Estimation Using Adaptive Search of Transformation Space,” 4713:204–13. Springer, 2007. https://doi.org/10.1007/978-3-540-74936-3_21.","ama":"Ulges A, Lampert C, Keysers D, Breuel T. Optimal dominant motion estimation using adaptive search of transformation space. In: Vol 4713. Springer; 2007:204-213. doi:10.1007/978-3-540-74936-3_21"},"day":"09","conference":{"name":"DAGM: German Association For Pattern Recognition"},"doi":"10.1007/978-3-540-74936-3_21"},{"doi":"10.1090/conm/412","conference":{"name":"Differential Equations and Mathematical Physics"},"day":"01","citation":{"apa":"Lieb, É., Seiringer, R., & Solovej, J. (2006). Ground-state energy of a dilute Fermi gas (Vol. 412, pp. 239–248). Presented at the Differential Equations and Mathematical Physics, American Mathematical Society. https://doi.org/10.1090/conm/412","short":"É. Lieb, R. Seiringer, J. Solovej, in:, American Mathematical Society, 2006, pp. 239–248.","mla":"Lieb, Élliott, et al. *Ground-State Energy of a Dilute Fermi Gas*. Vol. 412, American Mathematical Society, 2006, pp. 239–48, doi:10.1090/conm/412.","ieee":"É. Lieb, R. Seiringer, and J. Solovej, “Ground-state energy of a dilute Fermi gas,” presented at the Differential Equations and Mathematical Physics, 2006, vol. 412, pp. 239–248.","ista":"Lieb É, Seiringer R, Solovej J. 2006. Ground-state energy of a dilute Fermi gas. Differential Equations and Mathematical Physics, Contemporary Mathematics, vol. 412, 239–248.","ama":"Lieb É, Seiringer R, Solovej J. Ground-state energy of a dilute Fermi gas. In: Vol 412. American Mathematical Society; 2006:239-248. doi:10.1090/conm/412","chicago":"Lieb, Élliott, Robert Seiringer, and Jan Solovej. “Ground-State Energy of a Dilute Fermi Gas,” 412:239–48. American Mathematical Society, 2006. https://doi.org/10.1090/conm/412."},"publisher":"American Mathematical Society","title":"Ground-state energy of a dilute Fermi gas","quality_controlled":0,"page":"239 - 248","date_published":"2006-01-01T00:00:00Z","oa":1,"_id":"2333","month":"01","year":"2006","date_created":"2018-12-11T11:57:03Z","publication_status":"published","volume":412,"type":"conference","author":[{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"full_name":"Robert Seiringer","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan P"}],"date_updated":"2021-01-12T06:56:51Z","publist_id":"4593","alternative_title":["Contemporary Mathematics"],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0507049"}],"status":"public","extern":1,"intvolume":" 412"},{"title":"One-dimensional behavior of dilute, trapped Bose gases in traps","day":"07","citation":{"chicago":"Seiringer, Robert, Élliott Lieb, and Jakob Yngvason. “One-Dimensional Behavior of Dilute, Trapped Bose Gases in Traps.” edited by Jean Zambrini. World Scientific Publishing, 2006. https://doi.org/10.1007/s00220-003-0993-3.","ama":"Seiringer R, Lieb É, Yngvason J. One-dimensional behavior of dilute, trapped Bose gases in traps. In: Zambrini J, ed. World Scientific Publishing; 2006. doi:10.1007/s00220-003-0993-3","ieee":"R. Seiringer, É. Lieb, and J. Yngvason, “One-dimensional behavior of dilute, trapped Bose gases in traps,” presented at the ICMP: International Congress on Mathematical Physics, 2006.","ista":"Seiringer R, Lieb É, Yngvason J. 2006. One-dimensional behavior of dilute, trapped Bose gases in traps. ICMP: International Congress on Mathematical Physics.","mla":"Seiringer, Robert, et al. *One-Dimensional Behavior of Dilute, Trapped Bose Gases in Traps*. Edited by Jean Zambrini, World Scientific Publishing, 2006, doi:10.1007/s00220-003-0993-3.","apa":"Seiringer, R., Lieb, É., & Yngvason, J. (2006). One-dimensional behavior of dilute, trapped Bose gases in traps. In J. Zambrini (Ed.). Presented at the ICMP: International Congress on Mathematical Physics, World Scientific Publishing. https://doi.org/10.1007/s00220-003-0993-3","short":"R. Seiringer, É. Lieb, J. Yngvason, in:, J. Zambrini (Ed.), World Scientific Publishing, 2006."},"conference":{"name":"ICMP: International Congress on Mathematical Physics"},"doi":"10.1007/s00220-003-0993-3","publisher":"World Scientific Publishing","oa":1,"_id":"2334","quality_controlled":0,"date_published":"2006-03-07T00:00:00Z","type":"conference","editor":[{"full_name":"Zambrini, Jean-Claude","last_name":"Zambrini","first_name":"Jean"}],"year":"2006","month":"03","date_created":"2018-12-11T11:57:03Z","publication_status":"published","extern":1,"publist_id":"4592","date_updated":"2021-01-12T06:56:51Z","author":[{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Robert Seiringer"},{"last_name":"Lieb","full_name":"Lieb, Élliott H","first_name":"Élliott"},{"full_name":"Yngvason, Jakob","last_name":"Yngvason","first_name":"Jakob"}],"status":"public","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0305025","open_access":"1"}]},{"quality_controlled":0,"date_published":"2006-01-01T00:00:00Z","page":"505 - 537","oa":1,"_id":"2363","day":"01","citation":{"mla":"Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases.” *Communications in Mathematical Physics*, vol. 264, no. 2, Springer, 2006, pp. 505–37, doi:10.1007/s00220-006-1524-9.","ieee":"É. Lieb and R. Seiringer, “Derivation of the Gross-Pitaevskii equation for rotating Bose gases,” *Communications in Mathematical Physics*, vol. 264, no. 2. Springer, pp. 505–537, 2006.","ista":"Lieb É, Seiringer R. 2006. Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Communications in Mathematical Physics. 264(2), 505–537.","short":"É. Lieb, R. Seiringer, Communications in Mathematical Physics 264 (2006) 505–537.","apa":"Lieb, É., & Seiringer, R. (2006). Derivation of the Gross-Pitaevskii equation for rotating Bose gases. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-006-1524-9","chicago":"Lieb, Élliott, and Robert Seiringer. “Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases.” *Communications in Mathematical Physics*. Springer, 2006. https://doi.org/10.1007/s00220-006-1524-9.","ama":"Lieb É, Seiringer R. Derivation of the Gross-Pitaevskii equation for rotating Bose gases. *Communications in Mathematical Physics*. 2006;264(2):505-537. doi:10.1007/s00220-006-1524-9"},"doi":"10.1007/s00220-006-1524-9","publisher":"Springer","publication":"Communications in Mathematical Physics","title":"Derivation of the Gross-Pitaevskii equation for rotating Bose gases","abstract":[{"text":" We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. We have been able to overcome this difficulty with the aid of coherent states. Our proof also conceptually simplifies the previous proof for the slowly rotating case. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state. ","lang":"eng"}],"publist_id":"4561","date_updated":"2020-07-14T12:45:40Z","author":[{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Robert Seiringer"}],"status":"public","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0504042","open_access":"1"}],"issue":"2","intvolume":" 264","extern":1,"year":"2006","month":"01","volume":264,"date_created":"2018-12-11T11:57:13Z","publication_status":"published","type":"review"},{"volume":18,"publication_status":"published","date_created":"2018-12-11T11:57:14Z","month":"04","year":"2006","type":"journal_article","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0601051","open_access":"1"}],"status":"public","date_updated":"2021-01-12T06:57:02Z","author":[{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Robert Seiringer","last_name":"Seiringer"}],"publist_id":"4562","extern":1,"intvolume":" 18","issue":"3","publication":"Reviews in Mathematical Physics","publisher":"World Scientific Publishing","doi":"10.1142/S0129055X06002632","day":"01","citation":{"ama":"Seiringer R. A correlation estimate for quantum many-body systems at positive temperature. *Reviews in Mathematical Physics*. 2006;18(3):233-253. doi:10.1142/S0129055X06002632","chicago":"Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems at Positive Temperature.” *Reviews in Mathematical Physics*. World Scientific Publishing, 2006. https://doi.org/10.1142/S0129055X06002632.","apa":"Seiringer, R. (2006). A correlation estimate for quantum many-body systems at positive temperature. *Reviews in Mathematical Physics*. World Scientific Publishing. https://doi.org/10.1142/S0129055X06002632","short":"R. Seiringer, Reviews in Mathematical Physics 18 (2006) 233–253.","mla":"Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems at Positive Temperature.” *Reviews in Mathematical Physics*, vol. 18, no. 3, World Scientific Publishing, 2006, pp. 233–53, doi:10.1142/S0129055X06002632.","ieee":"R. Seiringer, “A correlation estimate for quantum many-body systems at positive temperature,” *Reviews in Mathematical Physics*, vol. 18, no. 3. World Scientific Publishing, pp. 233–253, 2006.","ista":"Seiringer R. 2006. A correlation estimate for quantum many-body systems at positive temperature. Reviews in Mathematical Physics. 18(3), 233–253."},"abstract":[{"text":"We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first-order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose-Einstein condensation.","lang":"eng"}],"title":"A correlation estimate for quantum many-body systems at positive temperature","page":"233 - 253","date_published":"2006-04-01T00:00:00Z","quality_controlled":0,"_id":"2364","oa":1},{"title":"The thermodynamic pressure of a dilute fermi gas","abstract":[{"text":"We consider a gas of fermions with non-zero spin at temperature T and chemical potential μ. We show that if the range of the interparticle interaction is small compared to the mean particle distance, the thermodynamic pressure differs to leading order from the corresponding expression for non-interacting particles by a term proportional to the scattering length of the interparticle interaction. This is true for any repulsive interaction, including hard cores. The result is uniform in the temperature as long as T is of the same order as the Fermi temperature, or smaller.","lang":"eng"}],"day":"01","citation":{"mla":"Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.” *Communications in Mathematical Physics*, vol. 261, no. 3, Springer, 2006, pp. 729–57, doi:10.1007/s00220-005-1433-3.","ieee":"R. Seiringer, “The thermodynamic pressure of a dilute fermi gas,” *Communications in Mathematical Physics*, vol. 261, no. 3. Springer, pp. 729–757, 2006.","ista":"Seiringer R. 2006. The thermodynamic pressure of a dilute fermi gas. Communications in Mathematical Physics. 261(3), 729–757.","short":"R. Seiringer, Communications in Mathematical Physics 261 (2006) 729–757.","apa":"Seiringer, R. (2006). The thermodynamic pressure of a dilute fermi gas. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-005-1433-3","chicago":"Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.” *Communications in Mathematical Physics*. Springer, 2006. https://doi.org/10.1007/s00220-005-1433-3.","ama":"Seiringer R. The thermodynamic pressure of a dilute fermi gas. *Communications in Mathematical Physics*. 2006;261(3):729-757. doi:10.1007/s00220-005-1433-3"},"doi":"10.1007/s00220-005-1433-3","publisher":"Springer","publication":"Communications in Mathematical Physics","oa":1,"_id":"2365","quality_controlled":0,"date_published":"2006-02-01T00:00:00Z","page":"729 - 757","type":"journal_article","year":"2006","month":"02","date_created":"2018-12-11T11:57:14Z","volume":261,"publication_status":"published","issue":"3","intvolume":" 261","extern":1,"publist_id":"4563","author":[{"last_name":"Seiringer","full_name":"Robert Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2021-01-12T06:57:02Z","status":"public","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0412086"}]},{"extern":1,"intvolume":" 77","issue":"3","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0605017","open_access":"1"}],"status":"public","date_updated":"2021-01-12T06:57:03Z","author":[{"first_name":"Rupert","last_name":"Frank","full_name":"Frank, Rupert L"},{"first_name":"Ari","full_name":"Laptev, Ari","last_name":"Laptev"},{"first_name":"Élliott","last_name":"Lieb","full_name":"Lieb, Élliott H"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Robert Seiringer"}],"publist_id":"4560","type":"journal_article","volume":77,"date_created":"2018-12-11T11:57:15Z","publication_status":"published","month":"09","year":"2006","_id":"2366","oa":1,"page":"309 - 316","date_published":"2006-09-01T00:00:00Z","quality_controlled":0,"abstract":[{"text":"Inequalities are derived for power sums of the real part and the modulus of the eigenvalues of a Schrödinger operator with a complex-valued potential.","lang":"eng"}],"title":"Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials","publisher":"Springer","publication":"Letters in Mathematical Physics","doi":"10.1007/s11005-006-0095-1","day":"01","citation":{"chicago":"Frank, Rupert, Ari Laptev, Élliott Lieb, and Robert Seiringer. “Lieb-Thirring Inequalities for Schrödinger Operators with Complex-Valued Potentials.” *Letters in Mathematical Physics*. Springer, 2006. https://doi.org/10.1007/s11005-006-0095-1.","ama":"Frank R, Laptev A, Lieb É, Seiringer R. Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. *Letters in Mathematical Physics*. 2006;77(3):309-316. doi:10.1007/s11005-006-0095-1","mla":"Frank, Rupert, et al. “Lieb-Thirring Inequalities for Schrödinger Operators with Complex-Valued Potentials.” *Letters in Mathematical Physics*, vol. 77, no. 3, Springer, 2006, pp. 309–16, doi:10.1007/s11005-006-0095-1.","ieee":"R. Frank, A. Laptev, É. Lieb, and R. Seiringer, “Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials,” *Letters in Mathematical Physics*, vol. 77, no. 3. Springer, pp. 309–316, 2006.","ista":"Frank R, Laptev A, Lieb É, Seiringer R. 2006. Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. Letters in Mathematical Physics. 77(3), 309–316.","short":"R. Frank, A. Laptev, É. Lieb, R. Seiringer, Letters in Mathematical Physics 77 (2006) 309–316.","apa":"Frank, R., Laptev, A., Lieb, É., & Seiringer, R. (2006). Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials. *Letters in Mathematical Physics*. Springer. https://doi.org/10.1007/s11005-006-0095-1"}},{"type":"book_chapter","editor":[{"full_name":"Dereziński, Jan","last_name":"Dereziński","first_name":"Jan"},{"full_name":"Siedentop, Heinz","last_name":"Siedentop","first_name":"Heinz"}],"publication_status":"published","volume":695,"date_created":"2018-12-11T11:57:15Z","year":"2006","month":"01","intvolume":" 695","extern":1,"status":"public","alternative_title":["LNP"],"publist_id":"4558","author":[{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Robert Seiringer","last_name":"Seiringer"}],"date_updated":"2021-01-12T06:57:03Z","abstract":[{"lang":"eng","text":"The recent experimental success in creating Bose-Einstein condensates of alkali atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest in the mathematical description of interacting Bose gases."}],"title":"Dilute, trapped Bose gases and Bose-Einstein condensation","publication":"Large Coulomb Systems","publisher":"Springer","citation":{"mla":"Seiringer, Robert. “Dilute, Trapped Bose Gases and Bose-Einstein Condensation.” *Large Coulomb Systems*, edited by Jan Dereziński and Heinz Siedentop, vol. 695, Springer, 2006, pp. 249–74, doi:10.1007/3-540-32579-4_6.","ieee":"R. Seiringer, “Dilute, trapped Bose gases and Bose-Einstein condensation,” in *Large Coulomb Systems*, vol. 695, J. Dereziński and H. Siedentop, Eds. Springer, 2006, pp. 249–274.","ista":"Seiringer R. 2006.Dilute, trapped Bose gases and Bose-Einstein condensation. In: Large Coulomb Systems. LNP, vol. 695, 249–274.","short":"R. Seiringer, in:, J. Dereziński, H. Siedentop (Eds.), Large Coulomb Systems, Springer, 2006, pp. 249–274.","apa":"Seiringer, R. (2006). Dilute, trapped Bose gases and Bose-Einstein condensation. In J. Dereziński & H. Siedentop (Eds.), *Large Coulomb Systems* (Vol. 695, pp. 249–274). Springer. https://doi.org/10.1007/3-540-32579-4_6","chicago":"Seiringer, Robert. “Dilute, Trapped Bose Gases and Bose-Einstein Condensation.” In *Large Coulomb Systems*, edited by Jan Dereziński and Heinz Siedentop, 695:249–74. Springer, 2006. https://doi.org/10.1007/3-540-32579-4_6.","ama":"Seiringer R. Dilute, trapped Bose gases and Bose-Einstein condensation. In: Dereziński J, Siedentop H, eds. *Large Coulomb Systems*. Vol 695. Springer; 2006:249-274. doi:10.1007/3-540-32579-4_6"},"day":"01","doi":"10.1007/3-540-32579-4_6","_id":"2368","date_published":"2006-01-01T00:00:00Z","page":"249 - 274","quality_controlled":0},{"quality_controlled":0,"date_published":"2006-01-01T00:00:00Z","page":"199 - 215","oa":1,"_id":"2369","day":"01","citation":{"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 *Mathematical Physics of Quantum Mechanics*, vol. 690, J. Asch and A. Joye, Eds. Springer, 2006, pp. 199–215.","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.","mla":"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.","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.","apa":"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","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 *Mathematical Physics of Quantum Mechanics*, edited by Joachim Asch and Alain Joye, 690:199–215. Springer, 2006. https://doi.org/10.1007/b11573432.","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. *Mathematical Physics of Quantum Mechanics*. Vol 690. Springer; 2006:199-215. doi:10.1007/b11573432"},"doi":"10.1007/b11573432","publisher":"Springer","publication":"Mathematical Physics of Quantum Mechanics","title":"Bose-Einstein condensation as a quantum phase transition in an optical lattice","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."}],"publist_id":"4559","author":[{"first_name":"Michael","full_name":"Aizenman, Michael","last_name":"Aizenman"},{"first_name":"Élliott","last_name":"Lieb","full_name":"Lieb, Élliott H"},{"last_name":"Seiringer","full_name":"Robert Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Jan","full_name":"Solovej, Jan P","last_name":"Solovej"},{"first_name":"Jakob","last_name":"Yngvason","full_name":"Yngvason, Jakob"}],"date_updated":"2021-01-12T06:57:04Z","status":"public","alternative_title":["LNP"],"main_file_link":[{"url":"http://arxiv.org/abs/cond-mat/0412034","open_access":"1"}],"intvolume":" 690","extern":1,"year":"2006","month":"01","volume":690,"publication_status":"published","date_created":"2018-12-11T11:57:16Z","type":"book_chapter","editor":[{"first_name":"Joachim","full_name":"Asch, Joachim","last_name":"Asch"},{"first_name":"Alain","last_name":"Joye","full_name":"Joye, Alain"}]},{"year":"2006","month":"01","date_created":"2018-12-11T11:57:32Z","publication_status":"published","volume":26,"type":"book_chapter","publist_id":"4509","author":[{"first_name":"Jørgen","full_name":"Bang-Jensen, Jørgen","last_name":"Bang Jensen"},{"full_name":"Reed, Bruce","last_name":"Reed","first_name":"Bruce"},{"first_name":"Bruce","last_name":"Schacht","full_name":"Schacht, Bruce"},{"last_name":"Šámal","full_name":"Šámal, Robert","first_name":"Robert"},{"first_name":"Bjarne","last_name":"Toft","full_name":"Toft, Bjarne"},{"orcid":"0000-0002-1494-0568","id":"36690CA2-F248-11E8-B48F-1D18A9856A87","first_name":"Uli","full_name":"Uli Wagner","last_name":"Wagner"}],"date_updated":"2021-01-12T06:57:21Z","status":"public","alternative_title":["Algorithms and Combinatorics"],"intvolume":" 26","extern":1,"citation":{"ama":"Bang Jensen J, Reed B, Schacht B, Šámal R, Toft B, Wagner U. On six problems posed by Jarik Nešetřil. In: *Topics in Discrete Mathematics*. Vol 26. Springer; 2006:613-627. doi:10.1007/3-540-33700-8_30","chicago":"Bang Jensen, Jørgen, Bruce Reed, Bruce Schacht, Robert Šámal, Bjarne Toft, and Uli Wagner. “On Six Problems Posed by Jarik Nešetřil.” In *Topics in Discrete Mathematics*, 26:613–27. Springer, 2006. https://doi.org/10.1007/3-540-33700-8_30.","short":"J. Bang Jensen, B. Reed, B. Schacht, R. Šámal, B. Toft, U. Wagner, in:, Topics in Discrete Mathematics, Springer, 2006, pp. 613–627.","apa":"Bang Jensen, J., Reed, B., Schacht, B., Šámal, R., Toft, B., & Wagner, U. (2006). On six problems posed by Jarik Nešetřil. In *Topics in Discrete Mathematics* (Vol. 26, pp. 613–627). Springer. https://doi.org/10.1007/3-540-33700-8_30","mla":"Bang Jensen, Jørgen, et al. “On Six Problems Posed by Jarik Nešetřil.” *Topics in Discrete Mathematics*, vol. 26, Springer, 2006, pp. 613–27, doi:10.1007/3-540-33700-8_30.","ieee":"J. Bang Jensen, B. Reed, B. Schacht, R. Šámal, B. Toft, and U. Wagner, “On six problems posed by Jarik Nešetřil,” in *Topics in Discrete Mathematics*, vol. 26, Springer, 2006, pp. 613–627.","ista":"Bang Jensen J, Reed B, Schacht B, Šámal R, Toft B, Wagner U. 2006.On six problems posed by Jarik Nešetřil. In: Topics in Discrete Mathematics. Algorithms and Combinatorics, vol. 26, 613–627."},"day":"01","doi":"10.1007/3-540-33700-8_30","publication":"Topics in Discrete Mathematics","publisher":"Springer","title":"On six problems posed by Jarik Nešetřil","quality_controlled":0,"date_published":"2006-01-01T00:00:00Z","page":"613 - 627","_id":"2416"}]