Mathematics of the BCS theory of superconductivity

by Prof. Christian Hainzl

Monday 19 Feb 2024, 09:00 → Thursday 22 Feb 2024, 11:00 Europe/Rome

Lecturer
Prof. Christian Hainzl (LMU)
hainzl AT math DOT lmu DOT de

Course description   
I will start with a short historical review of the development of the theoretical and experimental understanding of superconductivity leading up to the famous work of Bardeen-Cooper-Schrieffer (BCS). Transforming the BCS-functional into a mathematical functional of the free energy, I will first treat the translation invariant problem for general interaction potential, thereby deriving the BCS-gap equation in a general form.

This leads to the definition of the critical temperature via spectral theoretic means, and the formula for the critical temperature in the weak coupling case using a Birman-Schwinger argument. After that I will introduce external fields and present the main steps for the derivation of the Ginzburg-Landau functional (equation) close to the critical temperature.
 

References

T.B.A

Schedule
All lectures will be held at the Main Lecture Hall in Viale Crispi 7 building, according to the following schedule:

Tue   Feb 20:  9-11
Wed  Feb 21: 9-11
Thu   Feb 22:  9-11  & 14.30-16.30