Knowledge and understanding:
The aim of this course is to provide the basic theoretical knowledge on several aspects in quantum magnetism and the BCS theory of superconductivity. The most important physical theories will be studied in terms of logical and mathematical structure, of experimental evidences and physical phenomena.
Applying knowledge and understanding:
The student will achieve the capability to apply these notions to analyze magnetic phenomena and superconductivity and interpret them on the basis of the mathematical formulation of the physical laws.
By the end of the course, the student should be able to understand the physical phenomena related to quantum magnetism and superconductivity.
The student must be able to clearly present the basic concepts of quantum magnetism and of the BCS theory of superconductivity, together their consequences on observable phenomena.
Basic notions in Physics of Matter, Quantum Mechanics and Statistical Physics are required.
Course contents summary
The course is divided into two parts: the first part deals with several aspects in quantum magnetism, while the second part is focused the BCS theory of Superconductivity. In particular, the lecture cover the following subjects:
-Irreducible tensor operators.
-Direct exchange interaction-RKKY interaction-Superexchange interaction.
-Magnetic molecules-Strong exchange limit.
-Mean field theory in magnetic materials-Spin waves.
-Hubbard model-Stoner model.
-Kubo formula-Green functions.
-Cooper instability-Origin of the attractive interaction-BCS ground state-Canonical transformation-Predictions of the BCS theory.
-Condensed Matter Physics by M. P. Marder, Wiley.
-Quantum Theory of Magnetism by W. Nolting and A. Ramakanth, Springer.
-Lecture Notes on Electron Correlation and Magnetism by P. Fazekas, World Scientific.
-Introduction to superconductivity by M. Tinkham, Dover Publications.
Slides, blackboard calculations and numerical simulations.
Assessment methods and criteria
Oral examination on the topics of the course. The examination begins with the discussion of a subject chosen by the student. This part has a weight of about 1/3 in the final evaluation. This part of the examination is then followed by some questions on the other topics of the course.