The goal is to give a comprehensible introduction into the topics and methods of modern condensed matter theory. The course consists of two parts. The first one starts with an instruction on the nowadays `traditional´ diagrammatic technique supplemented by a detailed survey of the problems which are solved using this method, including Landau's theory of quantum liquids and BCS theory of superconductivity. The second part of the course deals with problems which require the use of more advanced non-perturbative approaches such as renormalisation group transformations, bosonization and Bethe Ansatz. These concepts will be introduced on the examples of quantum impurity problems such as potential scattering in Luttinger liquids, interedge tunnelling in fractional quantum Hall probes and Kondo effect in metals and mesoscopic quantum dots.

Tentative program:
  • Introductory materials: bosons, fermions and second quantisation
  • Green‘s functions approach
  • Exactly solvable problems: potential scattering, Luttinger liquids etc.
  • Theory of quantum fluids, BCS theory of superconductivity
  • Quantum impurity problems: Kondo effect, Anderson model, renormalisation group approach