{"year":"2008","day":"01","_id":"2380","page":"349 - 367","issue":"2","intvolume":"       281","doi":"10.1007/s00220-008-0489-2","quality_controlled":0,"date_created":"2018-12-11T11:57:20Z","date_updated":"2021-01-12T06:57:08Z","author":[{"full_name":"Hainzl, Christian","last_name":"Hainzl","first_name":"Christian"},{"full_name":"Hamza, Eman","last_name":"Hamza","first_name":"Eman"},{"full_name":"Robert Seiringer","first_name":"Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Solovej, Jan P","first_name":"Jan","last_name":"Solovej"}],"title":"The BCS functional for general pair interactions","date_published":"2008-07-01T00:00:00Z","status":"public","oa":1,"abstract":[{"lang":"eng","text":"The Bardeen-Cooper-Schrieffer (BCS) functional has recently received renewed attention as a description of fermionic gases interacting with local pairwise interactions. We present here a rigorous analysis of the BCS functional for general pair interaction potentials. For both zero and positive temperature, we show that the existence of a non-trivial solution of the nonlinear BCS gap equation is equivalent to the existence of a negative eigenvalue of a certain linear operator. From this we conclude the existence of a critical temperature below which the BCS pairing wave function does not vanish identically. For attractive potentials, we prove that the critical temperature is non-zero and exponentially small in the strength of the potential."}],"publication_status":"published","type":"journal_article","publist_id":"4547","publication":"Communications in Mathematical Physics","month":"07","publisher":"Springer","citation":{"ista":"Hainzl C, Hamza E, Seiringer R, Solovej J. 2008. The BCS functional for general pair interactions. Communications in Mathematical Physics. 281(2), 349–367.","mla":"Hainzl, Christian, et al. “The BCS Functional for General Pair Interactions.” <i>Communications in Mathematical Physics</i>, vol. 281, no. 2, Springer, 2008, pp. 349–67, doi:<a href=\"https://doi.org/10.1007/s00220-008-0489-2\">10.1007/s00220-008-0489-2</a>.","apa":"Hainzl, C., Hamza, E., Seiringer, R., &#38; Solovej, J. (2008). The BCS functional for general pair interactions. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-008-0489-2\">https://doi.org/10.1007/s00220-008-0489-2</a>","chicago":"Hainzl, Christian, Eman Hamza, Robert Seiringer, and Jan Solovej. “The BCS Functional for General Pair Interactions.” <i>Communications in Mathematical Physics</i>. Springer, 2008. <a href=\"https://doi.org/10.1007/s00220-008-0489-2\">https://doi.org/10.1007/s00220-008-0489-2</a>.","ama":"Hainzl C, Hamza E, Seiringer R, Solovej J. The BCS functional for general pair interactions. <i>Communications in Mathematical Physics</i>. 2008;281(2):349-367. doi:<a href=\"https://doi.org/10.1007/s00220-008-0489-2\">10.1007/s00220-008-0489-2</a>","short":"C. Hainzl, E. Hamza, R. Seiringer, J. Solovej, Communications in Mathematical Physics 281 (2008) 349–367.","ieee":"C. Hainzl, E. Hamza, R. Seiringer, and J. Solovej, “The BCS functional for general pair interactions,” <i>Communications in Mathematical Physics</i>, vol. 281, no. 2. Springer, pp. 349–367, 2008."},"volume":281,"extern":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/math-ph/0703086"}]}