[{"publist_id":"4562","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0601051"}],"doi":"10.1142/S0129055X06002632","publisher":"World Scientific Publishing","issue":"3","page":"233 - 253","date_created":"2018-12-11T11:57:14Z","publication_status":"published","quality_controlled":0,"author":[{"full_name":"Robert Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"citation":{"ieee":"R. Seiringer, “A correlation estimate for quantum many-body systems at positive temperature,” *Reviews in Mathematical Physics*, vol. 18, no. 3, 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.","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","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.","chicago":"Seiringer, Robert. “A Correlation Estimate for Quantum Many-Body Systems at Positive Temperature.” *Reviews in Mathematical Physics* 18, no. 3 (2006): 233–53. 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*, *18*(3), 233–253. https://doi.org/10.1142/S0129055X06002632"},"date_published":"2006-04-01T00:00:00Z","_id":"2364","day":"01","month":"04","type":"journal_article","oa":1,"publication":"Reviews in Mathematical Physics","status":"public","title":"A correlation estimate for quantum many-body systems at positive temperature","abstract":[{"lang":"eng","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."}],"year":"2006","extern":1,"date_updated":"2020-07-14T12:45:40Z","intvolume":" 18","volume":18},{"year":"2006","extern":1,"date_updated":"2020-07-14T12:45:40Z","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"}],"volume":261,"intvolume":" 261","publist_id":"4563","issue":"3","page":"729 - 757","publisher":"Springer","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0412086","open_access":"1"}],"doi":"10.1007/s00220-005-1433-3","quality_controlled":0,"author":[{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","first_name":"Robert"}],"citation":{"ista":"Seiringer R. 2006. The thermodynamic pressure of a dilute fermi gas. Communications in Mathematical Physics. 261(3), 729–757.","ieee":"R. Seiringer, “The thermodynamic pressure of a dilute fermi gas,” *Communications in Mathematical Physics*, vol. 261, no. 3, pp. 729–757, 2006.","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.","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","short":"R. Seiringer, Communications in Mathematical Physics 261 (2006) 729–757.","chicago":"Seiringer, Robert. “The Thermodynamic Pressure of a Dilute Fermi Gas.” *Communications in Mathematical Physics* 261, no. 3 (2006): 729–57. https://doi.org/10.1007/s00220-005-1433-3.","apa":"Seiringer, R. (2006). The thermodynamic pressure of a dilute fermi gas. *Communications in Mathematical Physics*, *261*(3), 729–757. https://doi.org/10.1007/s00220-005-1433-3"},"date_created":"2018-12-11T11:57:14Z","publication_status":"published","publication":"Communications in Mathematical Physics","status":"public","_id":"2365","day":"01","date_published":"2006-02-01T00:00:00Z","month":"02","oa":1,"type":"journal_article"},{"intvolume":" 77","volume":77,"title":"Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials","abstract":[{"lang":"eng","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."}],"date_updated":"2020-07-14T12:45:40Z","year":"2006","extern":1,"publication_status":"published","date_created":"2018-12-11T11:57:15Z","citation":{"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","short":"R. Frank, A. Laptev, É. Lieb, R. Seiringer, Letters in Mathematical Physics 77 (2006) 309–316.","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, 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.","apa":"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. https://doi.org/10.1007/s11005-006-0095-1","chicago":"Frank, Rupert, Ari Laptev, Élliott Lieb, and Robert Seiringer. “Lieb-Thirring Inequalities for Schrödinger Operators with Complex-Valued Potentials.” *Letters in Mathematical Physics* 77, no. 3 (2006): 309–16. https://doi.org/10.1007/s11005-006-0095-1."},"author":[{"first_name":"Rupert","full_name":"Frank, Rupert L","last_name":"Frank"},{"last_name":"Laptev","full_name":"Laptev, Ari","first_name":"Ari"},{"last_name":"Lieb","full_name":"Lieb, Élliott H","first_name":"Élliott"},{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","first_name":"Robert"}],"quality_controlled":0,"oa":1,"type":"journal_article","_id":"2366","date_published":"2006-09-01T00:00:00Z","month":"09","day":"01","status":"public","publication":"Letters in Mathematical Physics","publist_id":"4560","doi":"10.1007/s11005-006-0095-1","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0605017"}],"publisher":"Springer","page":"309 - 316","issue":"3"},{"publication_status":"published","date_created":"2018-12-11T11:57:15Z","citation":{"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.","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","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. Large Coulomb Systems. , LNP, vol. 695. 249–274.","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","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.","short":"R. Seiringer, in:, J. Dereziński, H. Siedentop (Eds.), Large Coulomb Systems, Springer, 2006, pp. 249–274."},"quality_controlled":0,"author":[{"last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer"}],"type":"book_chapter","month":"01","_id":"2368","day":"01","date_published":"2006-01-01T00:00:00Z","alternative_title":["LNP"],"status":"public","publication":"Large Coulomb Systems","publist_id":"4558","publisher":"Springer","doi":"10.1007/3-540-32579-4_6","page":"249 - 274","editor":[{"last_name":"Dereziński","first_name":"Jan","full_name":"Dereziński, Jan"},{"full_name":"Siedentop, Heinz","first_name":"Heinz","last_name":"Siedentop"}],"intvolume":" 695","volume":695,"title":"Dilute, trapped Bose gases and Bose-Einstein condensation","abstract":[{"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.","lang":"eng"}],"date_updated":"2020-07-14T12:45:40Z","year":"2006","extern":1},{"publication_status":"published","date_created":"2018-12-11T11:57:16Z","citation":{"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.","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","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. 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.","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"},"author":[{"last_name":"Aizenman","full_name":"Aizenman, Michael","first_name":"Michael"},{"last_name":"Lieb","full_name":"Lieb, Élliott H","first_name":"Élliott"},{"orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Jan","full_name":"Solovej, Jan P","last_name":"Solovej"},{"first_name":"Jakob","full_name":"Yngvason, Jakob","last_name":"Yngvason"}],"quality_controlled":0,"oa":1,"type":"book_chapter","day":"01","_id":"2369","date_published":"2006-01-01T00:00:00Z","month":"01","alternative_title":["LNP"],"status":"public","publication":"Mathematical Physics of Quantum Mechanics","publist_id":"4559","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/cond-mat/0412034"}],"publisher":"Springer","doi":"10.1007/b11573432","page":"199 - 215","editor":[{"last_name":"Asch","full_name":"Asch, Joachim","first_name":"Joachim"},{"first_name":"Alain","full_name":"Joye, Alain","last_name":"Joye"}],"intvolume":" 690","volume":690,"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."}],"date_updated":"2020-07-14T12:45:40Z","extern":1,"year":"2006"}]