[{"page":"119 - 138","date_published":"2012-05-01T00:00:00Z","quality_controlled":0,"title":"Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs","publisher":"Springer","publication":"Letters in Mathematical Physics","status":"public","intvolume":" 100","year":"2012","publication_status":"published","date_updated":"2021-01-12T06:57:14Z","oa":1,"author":[{"first_name":"Christian","full_name":"Hainzl, Christian","last_name":"Hainzl"},{"full_name":"Robert Seiringer","last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T11:57:25Z","main_file_link":[{"url":"http://arxiv.org/abs/1105.1100","open_access":"1"}],"issue":"2","citation":{"ista":"Hainzl C, Seiringer R. 2012. Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. Letters in Mathematical Physics. 100(2), 119–138.","ama":"Hainzl C, Seiringer R. Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. *Letters in Mathematical Physics*. 2012;100(2):119-138. doi:10.1007/s11005-011-0535-4","chicago":"Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs.” *Letters in Mathematical Physics*. Springer, 2012. https://doi.org/10.1007/s11005-011-0535-4.","short":"C. Hainzl, R. Seiringer, Letters in Mathematical Physics 100 (2012) 119–138.","ieee":"C. Hainzl and R. Seiringer, “Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs,” *Letters in Mathematical Physics*, vol. 100, no. 2. Springer, pp. 119–138, 2012.","apa":"Hainzl, C., & Seiringer, R. (2012). Low density limit of BCS theory and Bose-Einstein condensation of Fermion pairs. *Letters in Mathematical Physics*. Springer. https://doi.org/10.1007/s11005-011-0535-4","mla":"Hainzl, Christian, and Robert Seiringer. “Low Density Limit of BCS Theory and Bose-Einstein Condensation of Fermion Pairs.” *Letters in Mathematical Physics*, vol. 100, no. 2, Springer, 2012, pp. 119–38, doi:10.1007/s11005-011-0535-4."},"doi":"10.1007/s11005-011-0535-4","_id":"2397","volume":100,"day":"01","type":"journal_article","month":"05","abstract":[{"lang":"eng","text":"We consider the low-density limit of a Fermi gas in the BCS approximation. We show that if the interaction potential allows for a two-particle bound state, the system at zero temperature is well approximated by the Gross-Pitaevskii functional, describing a Bose-Einstein condensate of fermion pairs."}],"publist_id":"4530","extern":1},{"type":"review","day":"01","month":"07","volume":24,"_id":"2398","extern":1,"abstract":[{"lang":"eng","text":"We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time."}],"publist_id":"4528","main_file_link":[{"url":"http://arxiv.org/abs/1109.3804","open_access":"1"}],"author":[{"last_name":"Jakšić","full_name":"Jakšić, Vojkan","first_name":"Vojkan"},{"first_name":"Yoshiko","full_name":"Ogata, Yoshiko","last_name":"Ogata"},{"full_name":"Pillet, Claude A","last_name":"Pillet","first_name":"Claude"},{"last_name":"Seiringer","full_name":"Robert Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T11:57:26Z","doi":"10.1142/S0129055X12300026","issue":"6","citation":{"mla":"Jakšić, Vojkan, et al. “Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics.” *Reviews in Mathematical Physics*, vol. 24, no. 6, World Scientific Publishing, 2012, doi:10.1142/S0129055X12300026.","ieee":"V. Jakšić, Y. Ogata, C. Pillet, and R. Seiringer, “Quantum hypothesis testing and non-equilibrium statistical mechanics,” *Reviews in Mathematical Physics*, vol. 24, no. 6. World Scientific Publishing, 2012.","short":"V. Jakšić, Y. Ogata, C. Pillet, R. Seiringer, Reviews in Mathematical Physics 24 (2012).","apa":"Jakšić, V., Ogata, Y., Pillet, C., & Seiringer, R. (2012). Quantum hypothesis testing and non-equilibrium statistical mechanics. *Reviews in Mathematical Physics*. World Scientific Publishing. https://doi.org/10.1142/S0129055X12300026","chicago":"Jakšić, Vojkan, Yoshiko Ogata, Claude Pillet, and Robert Seiringer. “Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics.” *Reviews in Mathematical Physics*. World Scientific Publishing, 2012. https://doi.org/10.1142/S0129055X12300026.","ama":"Jakšić V, Ogata Y, Pillet C, Seiringer R. Quantum hypothesis testing and non-equilibrium statistical mechanics. *Reviews in Mathematical Physics*. 2012;24(6). doi:10.1142/S0129055X12300026","ista":"Jakšić V, Ogata Y, Pillet C, Seiringer R. 2012. Quantum hypothesis testing and non-equilibrium statistical mechanics. Reviews in Mathematical Physics. 24(6)."},"publication_status":"published","date_updated":"2020-07-14T12:45:40Z","publication":"Reviews in Mathematical Physics","status":"public","intvolume":" 24","year":"2012","oa":1,"date_published":"2012-07-01T00:00:00Z","title":"Quantum hypothesis testing and non-equilibrium statistical mechanics","publisher":"World Scientific Publishing","quality_controlled":0},{"status":"public","publication":"Quantum Many Body Systems","intvolume":" 2051","year":"2012","publication_status":"published","date_updated":"2021-01-12T06:57:14Z","page":"55 - 92","date_published":"2012-01-01T00:00:00Z","quality_controlled":0,"title":"Cold quantum gases and bose einstein condensation","publisher":"Springer","volume":2051,"_id":"2399","day":"01","type":"book_chapter","month":"01","abstract":[{"text":"Bose–Einstein condensation (BEC) in cold atomic gases was first achieved experimentally in 1995 [1, 6]. After initial failed attempts with spin-polarized atomic hydrogen, the first successful demonstrations of this phenomenon used gases of rubidium and sodium atoms, respectively. Since then there has been a surge of activity in this field, with ingenious experiments putting forth more and more astonishing results about the behavior of matter at very cold temperatures.\n","lang":"eng"}],"publist_id":"4526","extern":1,"author":[{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","last_name":"Seiringer"}],"alternative_title":["Lecture Notes in Mathematics"],"date_created":"2018-12-11T11:57:26Z","citation":{"ieee":"R. Seiringer, “Cold quantum gases and bose einstein condensation,” in *Quantum Many Body Systems*, vol. 2051, V. Rivasseau, R. Seiringer, J. Solovej, and T. Spencer, Eds. Springer, 2012, pp. 55–92.","short":"R. Seiringer, in:, V. Rivasseau, R. Seiringer, J. Solovej, T. Spencer (Eds.), Quantum Many Body Systems, Springer, 2012, pp. 55–92.","apa":"Seiringer, R. (2012). Cold quantum gases and bose einstein condensation. In V. Rivasseau, R. Seiringer, J. Solovej, & T. Spencer (Eds.), *Quantum Many Body Systems* (Vol. 2051, pp. 55–92). Springer. https://doi.org/10.1007/978-3-642-29511-9_2","mla":"Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.” *Quantum Many Body Systems*, edited by Vincent Rivasseau et al., vol. 2051, Springer, 2012, pp. 55–92, doi:10.1007/978-3-642-29511-9_2.","ama":"Seiringer R. Cold quantum gases and bose einstein condensation. In: Rivasseau V, Seiringer R, Solovej J, Spencer T, eds. *Quantum Many Body Systems*. Vol 2051. Springer; 2012:55-92. doi:10.1007/978-3-642-29511-9_2","chicago":"Seiringer, Robert. “Cold Quantum Gases and Bose Einstein Condensation.” In *Quantum Many Body Systems*, edited by Vincent Rivasseau, Robert Seiringer, Jan Solovej, and Thomas Spencer, 2051:55–92. Springer, 2012. https://doi.org/10.1007/978-3-642-29511-9_2.","ista":"Seiringer R. 2012.Cold quantum gases and bose einstein condensation. In: Quantum Many Body Systems. Lecture Notes in Mathematics, vol. 2051, 55–92."},"editor":[{"first_name":"Vincent","last_name":"Rivasseau","full_name":"Rivasseau, Vincent"},{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","full_name":"Robert Seiringer","last_name":"Seiringer"},{"full_name":"Solovej, Jan P","last_name":"Solovej","first_name":"Jan"},{"first_name":"Thomas","full_name":"Spencer, Thomas","last_name":"Spencer"}],"doi":"10.1007/978-3-642-29511-9_2"},{"date_created":"2018-12-11T11:45:23Z","author":[{"orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning","full_name":"Timothy Browning"},{"last_name":"Valckenborgh","full_name":"Valckenborgh, K Van","first_name":"K Van"}],"doi":"10.1080/10586458.2011.605733","citation":{"ama":"Browning TD, Valckenborgh KV. Sums of three squareful numbers. *Experimental Mathematics*. 2012;21(2):204-211. doi:10.1080/10586458.2011.605733","chicago":"Browning, Timothy D, and K Van Valckenborgh. “Sums of Three Squareful Numbers.” *Experimental Mathematics*. Taylor & Francis, 2012. https://doi.org/10.1080/10586458.2011.605733.","ista":"Browning TD, Valckenborgh KV. 2012. Sums of three squareful numbers. Experimental Mathematics. 21(2), 204–211.","mla":"Browning, Timothy D., and K. Van Valckenborgh. “Sums of Three Squareful Numbers.” *Experimental Mathematics*, vol. 21, no. 2, Taylor & Francis, 2012, pp. 204–11, doi:10.1080/10586458.2011.605733.","short":"T.D. Browning, K.V. Valckenborgh, Experimental Mathematics 21 (2012) 204–211.","apa":"Browning, T. D., & Valckenborgh, K. V. (2012). Sums of three squareful numbers. *Experimental Mathematics*. Taylor & Francis. https://doi.org/10.1080/10586458.2011.605733","ieee":"T. D. Browning and K. V. Valckenborgh, “Sums of three squareful numbers,” *Experimental Mathematics*, vol. 21, no. 2. Taylor & Francis, pp. 204–211, 2012."},"issue":"2","month":"05","type":"journal_article","day":"23","volume":21,"_id":"240","extern":1,"acknowledgement":"EP/E053262/1\tEngineering and Physical Sciences Research Council","publist_id":"7664","abstract":[{"lang":"eng","text":"We investigate the frequency of positive squareful numbers x, y, z≤B for which x+y=z and present a conjecture concerning its asymptotic behavior."}],"date_published":"2012-05-23T00:00:00Z","page":"204 - 211","publisher":"Taylor & Francis","title":"Sums of three squareful numbers","quality_controlled":0,"date_updated":"2021-01-12T06:57:15Z","publication_status":"published","year":"2012","intvolume":" 21","status":"public","publication":"Experimental Mathematics"},{"publisher":"Springer","title":"Binding of polarons and atoms at threshold","quality_controlled":0,"date_published":"2012-07-01T00:00:00Z","page":"405 - 424","oa":1,"date_updated":"2021-01-12T06:57:15Z","publication_status":"published","intvolume":" 313","year":"2012","publication":"Communications in Mathematical Physics","status":"public","doi":"10.1007/s00220-012-1436-9","citation":{"ista":"Frank R, Lieb É, Seiringer R. 2012. Binding of polarons and atoms at threshold. Communications in Mathematical Physics. 313(2), 405–424.","chicago":"Frank, Rupert, Élliott Lieb, and Robert Seiringer. “Binding of Polarons and Atoms at Threshold.” *Communications in Mathematical Physics*. Springer, 2012. https://doi.org/10.1007/s00220-012-1436-9.","ama":"Frank R, Lieb É, Seiringer R. Binding of polarons and atoms at threshold. *Communications in Mathematical Physics*. 2012;313(2):405-424. doi:10.1007/s00220-012-1436-9","short":"R. Frank, É. Lieb, R. Seiringer, Communications in Mathematical Physics 313 (2012) 405–424.","apa":"Frank, R., Lieb, É., & Seiringer, R. (2012). Binding of polarons and atoms at threshold. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-012-1436-9","ieee":"R. Frank, É. Lieb, and R. Seiringer, “Binding of polarons and atoms at threshold,” *Communications in Mathematical Physics*, vol. 313, no. 2. Springer, pp. 405–424, 2012.","mla":"Frank, Rupert, et al. “Binding of Polarons and Atoms at Threshold.” *Communications in Mathematical Physics*, vol. 313, no. 2, Springer, 2012, pp. 405–24, doi:10.1007/s00220-012-1436-9."},"issue":"2","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1106.0729"}],"date_created":"2018-12-11T11:57:27Z","author":[{"last_name":"Frank","full_name":"Frank, Rupert L","first_name":"Rupert"},{"first_name":"Élliott","last_name":"Lieb","full_name":"Lieb, Élliott H"},{"full_name":"Robert Seiringer","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert"}],"extern":1,"publist_id":"4527","abstract":[{"text":"If the polaron coupling constant α is large enough, bipolarons or multi-polarons will form. When passing through the critical α c from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explode? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at α c. Similarly, we show that the same phenomenon occurs for atoms, e. g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schrödinger equation, and are very general. They use the fact that the Coulomb repulsion decays like 1/r, while 'uncertainty principle' localization energies decay more rapidly, as 1/r 2.","lang":"eng"}],"month":"07","type":"journal_article","day":"01","_id":"2400","volume":313}]