[{"year":"2014","oa_version":"None","issue":"7","title":"Introduction","article_number":"075101","doi":"10.1063/1.4884877","date_updated":"2021-01-12T06:53:25Z","author":[{"full_name":"Jakšić, Vojkan","first_name":"Vojkan","last_name":"Jakšić"},{"full_name":"Pillet, Claude","last_name":"Pillet","first_name":"Claude"},{"first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"status":"public","intvolume":" 55","month":"07","_id":"1822","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","publication":"Journal of Mathematical Physics","language":[{"iso":"eng"}],"citation":{"mla":"Jakšić, Vojkan, et al. “Introduction.” *Journal of Mathematical Physics*, vol. 55, no. 7, 075101, American Institute of Physics, 2014, doi:10.1063/1.4884877.","short":"V. Jakšić, C. Pillet, R. Seiringer, Journal of Mathematical Physics 55 (2014).","ista":"Jakšić V, Pillet C, Seiringer R. 2014. Introduction. Journal of Mathematical Physics. 55(7), 075101.","ama":"Jakšić V, Pillet C, Seiringer R. Introduction. *Journal of Mathematical Physics*. 2014;55(7). doi:10.1063/1.4884877","ieee":"V. Jakšić, C. Pillet, and R. Seiringer, “Introduction,” *Journal of Mathematical Physics*, vol. 55, no. 7. American Institute of Physics, 2014.","chicago":"Jakšić, Vojkan, Claude Pillet, and Robert Seiringer. “Introduction.” *Journal of Mathematical Physics*. American Institute of Physics, 2014. https://doi.org/10.1063/1.4884877.","apa":"Jakšić, V., Pillet, C., & Seiringer, R. (2014). Introduction. *Journal of Mathematical Physics*. American Institute of Physics. https://doi.org/10.1063/1.4884877"},"quality_controlled":"1","date_created":"2018-12-11T11:54:12Z","type":"journal_article","date_published":"2014-07-01T00:00:00Z","day":"01","publication_status":"published","publisher":"American Institute of Physics","publist_id":"5284","department":[{"_id":"RoSe"}],"scopus_import":1,"volume":55},{"publication":"Reviews in Mathematical Physics","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Bräunlich, Gerhard, et al. “Translation-Invariant Quasi-Free States for Fermionic Systems and the BCS Approximation.” *Reviews in Mathematical Physics*, vol. 26, no. 7, 1450012, World Scientific Publishing, 2014, doi:10.1142/S0129055X14500123.","short":"G. Bräunlich, C. Hainzl, R. Seiringer, Reviews in Mathematical Physics 26 (2014).","ista":"Bräunlich G, Hainzl C, Seiringer R. 2014. Translation-invariant quasi-free states for fermionic systems and the BCS approximation. Reviews in Mathematical Physics. 26(7), 1450012.","ama":"Bräunlich G, Hainzl C, Seiringer R. Translation-invariant quasi-free states for fermionic systems and the BCS approximation. *Reviews in Mathematical Physics*. 2014;26(7). doi:10.1142/S0129055X14500123","ieee":"G. Bräunlich, C. Hainzl, and R. Seiringer, “Translation-invariant quasi-free states for fermionic systems and the BCS approximation,” *Reviews in Mathematical Physics*, vol. 26, no. 7. World Scientific Publishing, 2014.","chicago":"Bräunlich, Gerhard, Christian Hainzl, and Robert Seiringer. “Translation-Invariant Quasi-Free States for Fermionic Systems and the BCS Approximation.” *Reviews in Mathematical Physics*. World Scientific Publishing, 2014. https://doi.org/10.1142/S0129055X14500123.","apa":"Bräunlich, G., Hainzl, C., & Seiringer, R. (2014). Translation-invariant quasi-free states for fermionic systems and the BCS approximation. *Reviews in Mathematical Physics*. World Scientific Publishing. https://doi.org/10.1142/S0129055X14500123"},"quality_controlled":"1","language":[{"iso":"eng"}],"type":"journal_article","date_created":"2018-12-11T11:54:33Z","date_published":"2014-08-01T00:00:00Z","day":"01","publication_status":"published","publisher":"World Scientific Publishing","main_file_link":[{"url":"http://arxiv.org/abs/1305.5135","open_access":"1"}],"publist_id":"5206","department":[{"_id":"RoSe"}],"volume":26,"scopus_import":1,"abstract":[{"lang":"eng","text":"We study translation-invariant quasi-free states for a system of fermions with two-particle interactions. The associated energy functional is similar to the BCS functional but also includes direct and exchange energies. We show that for suitable short-range interactions, these latter terms only lead to a renormalization of the chemical potential, with the usual properties of the BCS functional left unchanged. Our analysis thus represents a rigorous justification of part of the BCS approximation. We give bounds on the critical temperature below which the system displays superfluidity."}],"oa":1,"year":"2014","issue":"7","oa_version":"Submitted Version","title":"Translation-invariant quasi-free states for fermionic systems and the BCS approximation","date_updated":"2021-01-12T06:53:52Z","doi":"10.1142/S0129055X14500123","article_number":"1450012","author":[{"first_name":"Gerhard","last_name":"Bräunlich","full_name":"Bräunlich, Gerhard"},{"first_name":"Christian","last_name":"Hainzl","full_name":"Hainzl, Christian"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"status":"public","intvolume":" 26","_id":"1889","month":"08"},{"publication_status":"published","publisher":"European Mathematical Society","publication":"Journal of the European Mathematical Society","quality_controlled":"1","date_created":"2018-12-11T11:54:38Z","type":"journal_article","date_published":"2014-08-23T00:00:00Z","publist_id":"5191","department":[{"_id":"RoSe"}],"scopus_import":1,"date_updated":"2021-01-12T06:53:58Z","oa":1,"issue":"7","title":"Strichartz inequality for orthonormal functions","month":"08","author":[{"first_name":"Rupert","last_name":"Frank","full_name":"Frank, Rupert"},{"first_name":"Mathieu","last_name":"Lewin","full_name":"Lewin, Mathieu"},{"full_name":"Lieb, Élliott","first_name":"Élliott","last_name":"Lieb"},{"first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"status":"public","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1306.1309"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"citation":{"ieee":"R. Frank, M. Lewin, É. Lieb, and R. Seiringer, “Strichartz inequality for orthonormal functions,” *Journal of the European Mathematical Society*, vol. 16, no. 7. European Mathematical Society, pp. 1507–1526, 2014.","ama":"Frank R, Lewin M, Lieb É, Seiringer R. Strichartz inequality for orthonormal functions. *Journal of the European Mathematical Society*. 2014;16(7):1507-1526. doi:10.4171/JEMS/467","chicago":"Frank, Rupert, Mathieu Lewin, Élliott Lieb, and Robert Seiringer. “Strichartz Inequality for Orthonormal Functions.” *Journal of the European Mathematical Society*. European Mathematical Society, 2014. https://doi.org/10.4171/JEMS/467.","apa":"Frank, R., Lewin, M., Lieb, É., & Seiringer, R. (2014). Strichartz inequality for orthonormal functions. *Journal of the European Mathematical Society*. European Mathematical Society. https://doi.org/10.4171/JEMS/467","short":"R. Frank, M. Lewin, É. Lieb, R. Seiringer, Journal of the European Mathematical Society 16 (2014) 1507–1526.","ista":"Frank R, Lewin M, Lieb É, Seiringer R. 2014. Strichartz inequality for orthonormal functions. Journal of the European Mathematical Society. 16(7), 1507–1526.","mla":"Frank, Rupert, et al. “Strichartz Inequality for Orthonormal Functions.” *Journal of the European Mathematical Society*, vol. 16, no. 7, European Mathematical Society, 2014, pp. 1507–26, doi:10.4171/JEMS/467."},"day":"23","project":[{"name":"NSERC Postdoctoral fellowship","_id":"26450934-B435-11E9-9278-68D0E5697425"}],"volume":16,"page":"1507 - 1526","doi":"10.4171/JEMS/467","abstract":[{"lang":"eng","text":"We prove a Strichartz inequality for a system of orthonormal functions, with an optimal behavior of the constant in the limit of a large number of functions. The estimate generalizes the usual Strichartz inequality, in the same fashion as the Lieb-Thirring inequality generalizes the Sobolev inequality. As an application, we consider the Schrödinger equation with a time-dependent potential and we show the existence of the wave operator in Schatten spaces."}],"year":"2014","oa_version":"Submitted Version","intvolume":" 16","_id":"1904"},{"month":"02","author":[{"full_name":"Bellazzini, Jacopo","last_name":"Bellazzini","first_name":"Jacopo"},{"first_name":"Rupert","last_name":"Frank","full_name":"Frank, Rupert"},{"first_name":"Élliott","last_name":"Lieb","full_name":"Lieb, Élliott"},{"orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"status":"public","date_updated":"2021-01-12T06:54:04Z","article_number":"1350021","issue":"1","oa":1,"title":"Existence of ground states for negative ions at the binding threshold","department":[{"_id":"RoSe"}],"publist_id":"5176","scopus_import":1,"publisher":"World Scientific Publishing","publication_status":"published","quality_controlled":"1","publication":"Reviews in Mathematical Physics","date_published":"2014-02-01T00:00:00Z","type":"journal_article","date_created":"2018-12-11T11:54:42Z","intvolume":" 26","_id":"1918","doi":"10.1142/S0129055X13500219","oa_version":"Submitted Version","year":"2014","abstract":[{"text":"As the nuclear charge Z is continuously decreased an N-electron atom undergoes a binding-unbinding transition. We investigate whether the electrons remain bound and whether the radius of the system stays finite as the critical value Zc is approached. Existence of a ground state at Zc is shown under the condition Zc < N-K, where K is the maximal number of electrons that can be removed at Zc without changing the energy.","lang":"eng"}],"project":[{"name":"NSERC Postdoctoral fellowship","_id":"26450934-B435-11E9-9278-68D0E5697425"}],"volume":26,"main_file_link":[{"url":"http://arxiv.org/abs/1301.5370","open_access":"1"}],"language":[{"iso":"eng"}],"citation":{"ista":"Bellazzini J, Frank R, Lieb É, Seiringer R. 2014. Existence of ground states for negative ions at the binding threshold. Reviews in Mathematical Physics. 26(1), 1350021.","short":"J. Bellazzini, R. Frank, É. Lieb, R. Seiringer, Reviews in Mathematical Physics 26 (2014).","mla":"Bellazzini, Jacopo, et al. “Existence of Ground States for Negative Ions at the Binding Threshold.” *Reviews in Mathematical Physics*, vol. 26, no. 1, 1350021, World Scientific Publishing, 2014, doi:10.1142/S0129055X13500219.","ieee":"J. Bellazzini, R. Frank, É. Lieb, and R. Seiringer, “Existence of ground states for negative ions at the binding threshold,” *Reviews in Mathematical Physics*, vol. 26, no. 1. World Scientific Publishing, 2014.","ama":"Bellazzini J, Frank R, Lieb É, Seiringer R. Existence of ground states for negative ions at the binding threshold. *Reviews in Mathematical Physics*. 2014;26(1). doi:10.1142/S0129055X13500219","apa":"Bellazzini, J., Frank, R., Lieb, É., & Seiringer, R. (2014). Existence of ground states for negative ions at the binding threshold. *Reviews in Mathematical Physics*. World Scientific Publishing. https://doi.org/10.1142/S0129055X13500219","chicago":"Bellazzini, Jacopo, Rupert Frank, Élliott Lieb, and Robert Seiringer. “Existence of Ground States for Negative Ions at the Binding Threshold.” *Reviews in Mathematical Physics*. World Scientific Publishing, 2014. https://doi.org/10.1142/S0129055X13500219."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","day":"01"},{"volume":331,"scopus_import":1,"publist_id":"5159","department":[{"_id":"RoSe"}],"main_file_link":[{"url":"http://arxiv.org/abs/1304.6344","open_access":"1"}],"publication_status":"published","publisher":"Springer","date_created":"2018-12-11T11:54:48Z","type":"journal_article","date_published":"2014-08-01T00:00:00Z","day":"01","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","publication":"Communications in Mathematical Physics","citation":{"apa":"Giuliani, A., Lieb, É., & Seiringer, R. (2014). Formation of stripes and slabs near the ferromagnetic transition. *Communications in Mathematical Physics*. Springer. https://doi.org/10.1007/s00220-014-1923-2","chicago":"Giuliani, Alessandro, Élliott Lieb, and Robert Seiringer. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” *Communications in Mathematical Physics*. Springer, 2014. https://doi.org/10.1007/s00220-014-1923-2.","ama":"Giuliani A, Lieb É, Seiringer R. Formation of stripes and slabs near the ferromagnetic transition. *Communications in Mathematical Physics*. 2014;331(1):333-350. doi:10.1007/s00220-014-1923-2","ieee":"A. Giuliani, É. Lieb, and R. Seiringer, “Formation of stripes and slabs near the ferromagnetic transition,” *Communications in Mathematical Physics*, vol. 331, no. 1. Springer, pp. 333–350, 2014.","mla":"Giuliani, Alessandro, et al. “Formation of Stripes and Slabs near the Ferromagnetic Transition.” *Communications in Mathematical Physics*, vol. 331, no. 1, Springer, 2014, pp. 333–50, doi:10.1007/s00220-014-1923-2.","ista":"Giuliani A, Lieb É, Seiringer R. 2014. Formation of stripes and slabs near the ferromagnetic transition. Communications in Mathematical Physics. 331(1), 333–350.","short":"A. Giuliani, É. Lieb, R. Seiringer, Communications in Mathematical Physics 331 (2014) 333–350."},"language":[{"iso":"eng"}],"quality_controlled":"1","month":"08","_id":"1935","intvolume":" 331","status":"public","author":[{"full_name":"Giuliani, Alessandro","last_name":"Giuliani","first_name":"Alessandro"},{"full_name":"Lieb, Élliott","last_name":"Lieb","first_name":"Élliott"},{"last_name":"Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2021-01-12T06:54:11Z","page":"333 - 350","doi":"10.1007/s00220-014-1923-2","title":"Formation of stripes and slabs near the ferromagnetic transition","oa":1,"abstract":[{"text":"We consider Ising models in d = 2 and d = 3 dimensions with nearest neighbor ferromagnetic and long-range antiferromagnetic interactions, the latter decaying as (distance)-p, p > 2d, at large distances. If the strength J of the ferromagnetic interaction is larger than a critical value J c, then the ground state is homogeneous. It has been conjectured that when J is smaller than but close to J c, the ground state is periodic and striped, with stripes of constant width h = h(J), and h → ∞ as J → Jc -. (In d = 3 stripes mean slabs, not columns.) Here we rigorously prove that, if we normalize the energy in such a way that the energy of the homogeneous state is zero, then the ratio e 0(J)/e S(J) tends to 1 as J → Jc -, with e S(J) being the energy per site of the optimal periodic striped/slabbed state and e 0(J) the actual ground state energy per site of the system. Our proof comes with explicit bounds on the difference e 0(J)-e S(J) at small but positive J c-J, and also shows that in this parameter range the ground state is striped/slabbed in a certain sense: namely, if one looks at a randomly chosen window, of suitable size ℓ (very large compared to the optimal stripe size h(J)), one finds a striped/slabbed state with high probability.","lang":"eng"}],"year":"2014","issue":"1","oa_version":"Submitted Version"}]