{"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/0801.4159"}],"author":[{"last_name":"Hainzl","full_name":"Hainzl, Christian","first_name":"Christian"},{"full_name":"Robert Seiringer","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"}],"extern":1,"publist_id":"4550","quality_controlled":0,"date_published":"2008-05-28T00:00:00Z","year":"2008","day":"28","status":"public","date_created":"2018-12-11T11:57:18Z","abstract":[{"text":"We derive upper and lower bounds on the critical temperature Tc and the energy gap Ξ (at zero temperature) for the BCS gap equation, describing spin- 1 2 fermions interacting via a local two-body interaction potential λV(x). At weak coupling λ 1 and under appropriate assumptions on V(x), our bounds show that Tc ∼A exp(-B/λ) and Ξ∼C exp(-B/λ) for some explicit coefficients A, B, and C depending on the interaction V(x) and the chemical potential μ. The ratio A/C turns out to be a universal constant, independent of both V(x) and μ. Our analysis is valid for any μ; for small μ, or low density, our formulas reduce to well-known expressions involving the scattering length of V(x).","lang":"eng"}],"intvolume":"        77","publication":"Physical Review B - Condensed Matter and Materials Physics","date_updated":"2021-01-12T06:57:06Z","citation":{"apa":"Hainzl, C., &#38; Seiringer, R. (2008). Critical temperature and energy gap for the BCS equation. <i>Physical Review B - Condensed Matter and Materials Physics</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevB.77.184517\">https://doi.org/10.1103/PhysRevB.77.184517</a>","short":"C. Hainzl, R. Seiringer, Physical Review B - Condensed Matter and Materials Physics 77 (2008).","ieee":"C. Hainzl and R. Seiringer, “Critical temperature and energy gap for the BCS equation,” <i>Physical Review B - Condensed Matter and Materials Physics</i>, vol. 77, no. 18. American Physical Society, 2008.","chicago":"Hainzl, Christian, and Robert Seiringer. “Critical Temperature and Energy Gap for the BCS Equation.” <i>Physical Review B - Condensed Matter and Materials Physics</i>. American Physical Society, 2008. <a href=\"https://doi.org/10.1103/PhysRevB.77.184517\">https://doi.org/10.1103/PhysRevB.77.184517</a>.","mla":"Hainzl, Christian, and Robert Seiringer. “Critical Temperature and Energy Gap for the BCS Equation.” <i>Physical Review B - Condensed Matter and Materials Physics</i>, vol. 77, no. 18, American Physical Society, 2008, doi:<a href=\"https://doi.org/10.1103/PhysRevB.77.184517\">10.1103/PhysRevB.77.184517</a>.","ama":"Hainzl C, Seiringer R. Critical temperature and energy gap for the BCS equation. <i>Physical Review B - Condensed Matter and Materials Physics</i>. 2008;77(18). doi:<a href=\"https://doi.org/10.1103/PhysRevB.77.184517\">10.1103/PhysRevB.77.184517</a>","ista":"Hainzl C, Seiringer R. 2008. Critical temperature and energy gap for the BCS equation. Physical Review B - Condensed Matter and Materials Physics. 77(18)."},"type":"journal_article","month":"05","issue":"18","title":"Critical temperature and energy gap for the BCS equation","_id":"2376","doi":"10.1103/PhysRevB.77.184517","publication_status":"published","volume":77,"publisher":"American Physical Society","oa":1}