[{"alternative_title":["Contemporary Mathematics"],"doi":"10.1090/conm/412","conference":{"name":"Differential Equations and Mathematical Physics"},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0507049"}],"day":"01","page":"239 - 248","extern":1,"type":"conference","_id":"2333","oa":1,"citation":{"short":"É. Lieb, R. Seiringer, J. Solovej, in:, American Mathematical Society, 2006, pp. 239–248.","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.","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","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","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.","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.","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."},"author":[{"last_name":"Lieb","full_name":"Lieb, Élliott H","first_name":"Élliott"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","last_name":"Seiringer"},{"first_name":"Jan","full_name":"Solovej, Jan P","last_name":"Solovej"}],"quality_controlled":0,"date_published":"2006-01-01T00:00:00Z","title":"Ground-state energy of a dilute Fermi gas","month":"01","date_updated":"2021-01-12T06:56:51Z","status":"public","date_created":"2018-12-11T11:57:03Z","publication_status":"published","year":"2006","publist_id":"4593","intvolume":" 412","volume":412,"publisher":"American Mathematical Society"},{"doi":"10.1007/s00220-003-0993-3","editor":[{"first_name":"Jean","full_name":"Zambrini, Jean-Claude","last_name":"Zambrini"}],"conference":{"name":"ICMP: International Congress on Mathematical Physics"},"main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0305025","open_access":"1"}],"day":"07","extern":1,"_id":"2334","type":"conference","citation":{"short":"R. Seiringer, É. Lieb, J. Yngvason, in:, J. Zambrini (Ed.), World Scientific Publishing, 2006.","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.","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.","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","ista":"Seiringer R, Lieb É, Yngvason J. 2006. One-dimensional behavior of dilute, trapped Bose gases in traps. ICMP: International Congress on Mathematical Physics.","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"},"author":[{"last_name":"Seiringer","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"},{"full_name":"Lieb, Élliott H","last_name":"Lieb","first_name":"Élliott"},{"first_name":"Jakob","full_name":"Yngvason, Jakob","last_name":"Yngvason"}],"oa":1,"quality_controlled":0,"title":"One-dimensional behavior of dilute, trapped Bose gases in traps","date_published":"2006-03-07T00:00:00Z","date_created":"2018-12-11T11:57:03Z","status":"public","date_updated":"2021-01-12T06:56:51Z","publication_status":"published","month":"03","publist_id":"4592","year":"2006","publisher":"World Scientific Publishing"},{"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0504042"}],"doi":"10.1007/s00220-006-1524-9","issue":"2","extern":1,"type":"review","_id":"2363","day":"01","page":"505 - 537","publication":"Communications in Mathematical Physics","date_published":"2006-01-01T00:00:00Z","title":"Derivation of the Gross-Pitaevskii equation for rotating Bose gases","author":[{"first_name":"Élliott","full_name":"Lieb, Élliott H","last_name":"Lieb"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"oa":1,"citation":{"short":"É. Lieb, R. Seiringer, Communications in Mathematical Physics 264 (2006) 505–537.","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.","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","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","ista":"Lieb É, Seiringer R. 2006. Derivation of the Gross-Pitaevskii equation for rotating Bose gases. Communications in Mathematical Physics. 264(2), 505–537.","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.","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."},"quality_controlled":0,"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. "}],"year":"2006","publist_id":"4561","intvolume":" 264","volume":264,"publisher":"Springer","month":"01","publication_status":"published","date_created":"2018-12-11T11:57:13Z","status":"public","date_updated":"2020-07-14T12:45:40Z"},{"page":"233 - 253","day":"01","type":"journal_article","_id":"2364","extern":1,"issue":"3","doi":"10.1142/S0129055X06002632","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0601051"}],"month":"04","date_updated":"2021-01-12T06:57:02Z","publication_status":"published","status":"public","date_created":"2018-12-11T11:57:14Z","volume":18,"intvolume":" 18","publisher":"World Scientific Publishing","year":"2006","publist_id":"4562","quality_controlled":0,"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"}],"author":[{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","first_name":"Robert","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. World Scientific Publishing, pp. 233–253, 2006.","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*. 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","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"},"oa":1,"date_published":"2006-04-01T00:00:00Z","publication":"Reviews in Mathematical Physics","title":"A correlation estimate for quantum many-body systems at positive temperature"},{"month":"02","date_created":"2018-12-11T11:57:14Z","date_updated":"2021-01-12T06:57:02Z","status":"public","publication_status":"published","year":"2006","publist_id":"4563","volume":261,"intvolume":" 261","publisher":"Springer","author":[{"orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"oa":1,"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","ista":"Seiringer R. 2006. The thermodynamic pressure of a dilute fermi gas. Communications in Mathematical Physics. 261(3), 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","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.","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.","short":"R. Seiringer, Communications in Mathematical Physics 261 (2006) 729–757.","ieee":"R. Seiringer, “The thermodynamic pressure of a dilute fermi gas,” *Communications in Mathematical Physics*, vol. 261, no. 3. Springer, pp. 729–757, 2006."},"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."}],"quality_controlled":0,"date_published":"2006-02-01T00:00:00Z","publication":"Communications in Mathematical Physics","title":"The thermodynamic pressure of a dilute fermi gas","day":"01","page":"729 - 757","extern":1,"type":"journal_article","_id":"2365","doi":"10.1007/s00220-005-1433-3","issue":"3","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0412086","open_access":"1"}]}]