FYSS5550 Kollektiiviset kvantti-ilmiöt tiiviin aineen fysiikassa (5 op)

• Second quantization, causal, retarded and advanced Green’s function of the many-body system. Free fermion and phonon propagators. Relation to observables. Connection between different types of the Green’s functions: retarded/advanced, real-time and imaginary time.

• Concept of quasiparticles

• Perturbation theory: Wick’s theorem, Feynman rules. Self-energy, Dyson’s equation, polarization operator. Example of Coulomb screening and plasma waves

• Hartree-Fock approximation, ground state energy of interacting system, stability of metals and Stoner criterion of magnetism

• Fermi liquid theory: susceptibilities, zero sound and spin waves

• Methods of the many-body theory in superconductivity. Cooper problem and pairing instability in particle-hole channel Green’s functions of a superconductor. Gor’kov equations, Bogolubov-de Gennes equations. Quasiparticles in superconductors.

• Ginzburg-Landau theory, Meissner effect, Abrikosov vortices and Anderson-Higgs mechanism.

• Magnetism in Hubbard model

• Antiferromanetism

• Bose systems: condensation, superfluidity in weakly interacting Bose gas. Gross-Pitaevskii equation. 

At the end of this course, students will be able to

• Explain the role of interactions in many-body systems: electron in metals, atoms in quantum liquids and gases

• Explain the most common models of many-body systems such as the concepts of quasiparticles, Hartree-Fock approximation, Fermi liquid theory, Hubbard model

• Use basic theoretical tools such as the second quantization formalism, many-body Green's functions and Feynman diagram technique

• Explain superconductivity in metals and superfluidity in quantum liquids. Apply BCS model and Ginzburg-Landau theory to describe magnetic and thermodynamic properties of superconductors.

• Use Stoner and Hubbard models to describe magnetic phenomena in metals.

• Give a presentation of the scientific paper related to the topics of the course 

Either of FYSS7630 Many-particle quantum mechanics, FYSS7641 Statistical physics in and out of equilibrium, FYSS4510 Quantum Field Theory, FYSS7531-FYSS7532 Quantum Mechanics 2, parts A&B. 

Textbooks, lecture slides and notes, excercises.