Syllabus
Lectures deal with the Fermi liquid of electrons in crystals. First we return to the classical Boltzmann equation which we use to introduce the interplay of the free drift and collisions of particles. We demonstrate the implentation of the theory on the proof of the entropy production by collisions. Moreover, we evaluate the pressure and share viscosity in gasses.
Second, we extend the Boltzmann equation to cover the plasma adding the
Lorentz force from a mean electromagnetic field. We derive the classical linear response and discuss non-trivial aspects of the interaction of wave with particles in the regime of the two-stream instability. Our phenomenologic presentation of the idea of the mean field is closed by the Landau concept of quasiparticles.
In the course of quantum generalization we first employ the Fermi Golden rule and Pauli exclussion principle in collisions. The quantum treatment of the drift requires to leave the Boltzmann distribution and handle the reduced density matrix instead. In this framework we derive the linear response and show that quantum systems reveal a classically prohibited feature ? at certain distances the repulsive Coulomb forces become attractive. This explains stability of metalic crystals.
Systematic approach to non-equlibrium many-body systems we base on the method of non-equilibrium Greens functions. We first develop Greens functions for the ground state for which we introduce the Feynman diagrammatic approach. Derived rules apply also at finite temperatures and for non-equilibrium systems. We interlink these cases with the help of the complex time path. From equations for the Green function we recover the
Boltzmann equation with all the above mentioned improovements.
Annotation
Quantum-statistical theory of non-equilibrium properties of crystals.