FYSS5550 Collective Quantum Phenomena in Condensed Matter Physics (5 cr)

Content

The course is an introduction into the basic topics studied by the modern condensed matter theory. The phenomena will be discussed that emerge when a large number of atoms are coupled together. The course consists of two parts. The first one is devoted to explain the basic formalism starting from the second quantization approach, the definition of many-body Green’s functions and the perturbation theory/ Feynman rules. During the second part of the course the general formalism will be applied to consider the following topics: 1) Landau Fermi liquid theory: the concept of quasiparticles, corrections to the physical quantities, collective modes, ferromagnetism and spin waves. Microscopic theory of the Fermi liquid. 2) Mean-field theory of superconductivity, Ginzburg-Landau theory, Meissner effect and Anderson-Higgs mechanism. 3) Bose–Einstein condensation and superfluidity in a weakly interacting Bose gas.

Course main content: 1) Second quantization, causal, retarded and advanced Green’s function of the many-body system. Free fermion and phonon propagators. 2) Relation to observables. Connection between different types of the Green’s functions: retarded/advanced, real-time and imaginary time. 3) Perturbation theory: Wick’s theorem, Feynman rules. Self energy, Dyson’s equation, polarization operator. Example of Coulomb screening. 4) Fermi liquid theory: the concept of quasiparticles. 5) Interaction between quasiparticles, Fermi liquid corrections to physical quantities. Stoner instability and ferromagnetism. 6) Methods of the many-body theory in superconductivity. General picture of the superconducting state. Cooper pairing and instability of the normal state. Green’s functions of a superconductor. 7) Gor’kov equations, Bogolubov-de Gennes equations. Quasiparticles in superconductors, Majorana fermions in condensed matter systems. 8) Ginzburg-Landau theory, Meissner effect, Abrikosov vortices and Anderson-Higgs mechanism. 9) Bose systems: condensation, superfluidity in weakly interacting Bose gas. Gross-Pitaevskii equation.

Completion methods

Lectures, exercises, assignments, group work, final project

The course will be carried out via lectures and exercise sessions. One part of the material will be delivered in the form of lectures. Before each lecture the pre-reading assignment is given with the material to be considered during the next class. The other part will be suggested for the self-studying. Students will be asked to form the groups and during each exercise session one of the groups will present the summary of a certain topic. This will earn points for the group members. A certain number of group presentations will be necessary to complete the course. Homework problems will be assigned every week or so.

Assessment details

Passing the course requires: (i) receiving enough (more than half) of the exercise points based on the electronic submissions and enough number of group presentations during the exercise sessions, (ii) completion of the final project which will be implemented based on the group work and the selection of the particular topic from the course based on the student’s choice.