FYSS5550 Kollektiiviset kvantti-ilmiöt tiiviin aineen fysiikassa

Kurssin sisältö

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.