--- _id: '2363' abstract: - lang: eng 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. ' author: - first_name: Élliott full_name: Lieb, Élliott H last_name: Lieb - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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 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. 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. 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. short: É. Lieb, R. Seiringer, Communications in Mathematical Physics 264 (2006) 505–537. date_created: 2018-12-11T11:57:13Z date_published: 2006-01-01T00:00:00Z date_updated: 2020-07-14T12:45:40Z day: '01' doi: 10.1007/s00220-006-1524-9 extern: 1 intvolume: ' 264' issue: '2' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math-ph/0504042 month: '01' oa: 1 page: 505 - 537 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '4561' quality_controlled: 0 status: public title: Derivation of the Gross-Pitaevskii equation for rotating Bose gases type: review volume: 264 year: '2006' ... --- _id: '2364' 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. author: - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 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 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 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. 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. 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. short: R. Seiringer, Reviews in Mathematical Physics 18 (2006) 233–253. date_created: 2018-12-11T11:57:14Z date_published: 2006-04-01T00:00:00Z date_updated: 2021-01-12T06:57:02Z day: '01' doi: 10.1142/S0129055X06002632 extern: 1 intvolume: ' 18' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math-ph/0601051 month: '04' oa: 1 page: 233 - 253 publication: Reviews in Mathematical Physics publication_status: published publisher: World Scientific Publishing publist_id: '4562' quality_controlled: 0 status: public title: A correlation estimate for quantum many-body systems at positive temperature type: journal_article volume: 18 year: '2006' ... --- _id: '2365' abstract: - lang: eng 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. author: - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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 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. 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. 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. short: R. Seiringer, Communications in Mathematical Physics 261 (2006) 729–757. date_created: 2018-12-11T11:57:14Z date_published: 2006-02-01T00:00:00Z date_updated: 2021-01-12T06:57:02Z day: '01' doi: 10.1007/s00220-005-1433-3 extern: 1 intvolume: ' 261' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math-ph/0412086 month: '02' oa: 1 page: 729 - 757 publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '4563' quality_controlled: 0 status: public title: The thermodynamic pressure of a dilute fermi gas type: journal_article volume: 261 year: '2006' ... --- _id: '2366' 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. author: - first_name: Rupert full_name: Frank, Rupert L last_name: Frank - first_name: Ari full_name: Laptev, Ari last_name: Laptev - first_name: Élliott full_name: Lieb, Élliott H last_name: Lieb - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 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 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 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. 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. 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. short: R. Frank, A. Laptev, É. Lieb, R. Seiringer, Letters in Mathematical Physics 77 (2006) 309–316. date_created: 2018-12-11T11:57:15Z date_published: 2006-09-01T00:00:00Z date_updated: 2021-01-12T06:57:03Z day: '01' doi: 10.1007/s11005-006-0095-1 extern: 1 intvolume: ' 77' issue: '3' main_file_link: - open_access: '1' url: http://arxiv.org/abs/math-ph/0605017 month: '09' oa: 1 page: 309 - 316 publication: Letters in Mathematical Physics publication_status: published publisher: Springer publist_id: '4560' quality_controlled: 0 status: public title: Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials type: journal_article volume: 77 year: '2006' ... --- _id: '2368' 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. alternative_title: - LNP author: - first_name: Robert full_name: Robert Seiringer id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: 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' 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. 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.' 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. date_created: 2018-12-11T11:57:15Z date_published: 2006-01-01T00:00:00Z date_updated: 2021-01-12T06:57:03Z day: '01' doi: 10.1007/3-540-32579-4_6 editor: - first_name: Jan full_name: Dereziński, Jan last_name: Dereziński - first_name: Heinz full_name: Siedentop, Heinz last_name: Siedentop extern: 1 intvolume: ' 695' month: '01' page: 249 - 274 publication: Large Coulomb Systems publication_status: published publisher: Springer publist_id: '4558' quality_controlled: 0 status: public title: Dilute, trapped Bose gases and Bose-Einstein condensation type: book_chapter volume: 695 year: '2006' ...