{"author":[{"full_name":"Hainzl, Christian","last_name":"Hainzl","first_name":"Christian"},{"first_name":"Eman","last_name":"Hamza","full_name":"Hamza, Eman"},{"orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Robert Seiringer","first_name":"Robert"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan P"}],"date_updated":"2021-01-12T06:57:08Z","month":"07","title":"The BCS functional for general pair interactions","doi":"10.1007/s00220-008-0489-2","_id":"2380","volume":281,"date_published":"2008-07-01T00:00:00Z","date_created":"2018-12-11T11:57:20Z","publication_status":"published","day":"01","publication":"Communications in Mathematical Physics","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.","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.","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>","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>.","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>.","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>"},"type":"journal_article","page":"349 - 367","status":"public","extern":1,"intvolume":"       281","publist_id":"4547","issue":"2","quality_controlled":0,"publisher":"Springer","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."}],"oa":1,"year":"2008","main_file_link":[{"url":"http://arxiv.org/abs/math-ph/0703086","open_access":"1"}]}