Equilibrium and Non-Equilibrium
diagrammatic techniques
for
many-particle systems
Priv. Doz. Dr. Mikhail Kiselev
2 hours per week (in English)
This lecture course is proposed
for the students starting from 6 Semester, interested in a Diploma Project in
theoretical physics. This course gives an introduction to modern methods of
theoretical physics (Feynman diagram technique, path integral representation, Schwinger-Keldysh formalism). The applications of
equilibrium and non-equilibrium (real-time) approaches for many-particle
systems will be illustrated by numerous examples (Fermi-liquid theory,
Bose-Einstein condensation, perturbation theory in mesoscopic
and nano-systems etc). The “language” of Feynman
diagrams is widely used in modern scientific publications and is very useful
both for the visualization of results of calculations of physical quantities
and the interpretation of various many-particle effects. The course will be
useful for students interested in theory of low-dimensional systems and
strongly correlated phenomena. It includes the following chapters:
- Methods of second quantization. Fermi and Bose
operators.
- Partition function. Path integral representation.
- Feynman diagram technique at zero temperature. Wick’s
theorem.
- Several examples of the application of diagrammatic technique
at T=0 (Coulomb interaction, magnetic correlations).
- Diagrammatic technique at finite temperatures
(Matsubara formalism). Path integral representation. Effective action
approach. “Fast” and “slow” variables. Plasmons
and excitons.
- Basic concepts of Fermi-liquid theory. Luttinger theorem. Ward identities.
- Bose-Einstein Condensation. Weakly interacting Bose
gas. Coulomb interaction in Bose-systems.
- Superfluidity and
superconductivity. Gor’kov equations.
- Diagrammatic technique for local spins. Schwinger bosons, pseudo-fermions, Hubbard operators,
semi-fermions. Kondo effect.
- Green’s functions in the theory of phase transitions.
Fluctuations. Critical dynamics. Scaling.
- Real-time (non-equilibrium) formalism. Path integral
representation. Keldysh contour. Kinetic
equation.
- Applications of non-equilibrium (Schwinger-Keldysh)
diagrammatic technique in mesoscopics.
Recommended literature:
- G.Mahan, Many-particle
physics (Plenum press, NY) 1993
- J.W.Negele and H.Orland, Quantum Many-Particle Systems (Addison
Wesley, Reading, MA),
1988
- A.Auerbach, Interacting
electrons and Quantum Magnetism (Springer-Verlag),
1994