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Summerschool on "Current Topics in Mathematical Physics"
Organizers: Maria Esteban (Paris Dauphine), Mathieu Lewin (Cergy) & Robert Seiringer (Vienna)


Christian Hainzl (Tuebingen, Germany) "The BCS-functional of superconductivity (superfluidity)" 4
Saturday 07 September 2013, 09:00 - 10:00
CIRM Marseille


Abstract: We start by analyzing the translation invariant BCS functional, and derive the non-linear BCS-gap equation. We show that the existence of a non-trivial solution is equivalent to a linear criterion. Applying methods of spectral theory, such as Birman-Schwinger type techniques, to the corresponding linear operator it is possible to evaluate the critical temperature.  Finally, we outline how the Ginzburg-Landau theory can be derived from the BCS functional close to the critical temperature via a semiclassical limit.