Many Body Physics (24 lectures)

Prof. Mikhail Kiselev 2010.

Lecture 1

Symmetries. Free fermions and Bosons. Distribution functions. Connection between spin and statistics.

Lecture 2

Ideal Fermi gas. Pauli principle. Quasiparticles. Fermi liquid. Quasiparticles lifetime. Luttinger theorem. Effects of interaction. Mass renormalization. Thermodynamics of Fermi systems.

Lecture 3

Magnetism of itinerant electrons. Pauli paramagnetism. Landau levels. Diamagnetism.

Lecture 4

Ideal Bose gas. Bose-Einstein condensation. Thermodynamics of IBG.

Lecture 5

Weakly interacting BG. Long-wave excitations in weakly interacting BG: phonons.

Goldstone theorem. Bogoliubov's transformation. Long-range order. Mermin-Wagner theorem.

Lecture 6

Superfluidity. Experimental observation. Non-classical inertia moments.

Thermo-mechanical effect. Rotons. Landau criterion. Vortices. Thermodynamics

of weakly interacting BG.

Lecture 7

Ultra-cold atomic and molecular gases. Optical lattices. BEC in traps.

Lecture 8

Localized magnetism: classification. Semi-classical theory of ferromagnetism.

Langevin function. Curie susceptibility. Molecular (Weiss) field. Critical temperature.

Curie-Weiss law.

Lecture 9

Quantum theory of ferromagnetism. Brillouin function. Critical temperature.

Curie and Curie-Weiss susceptibilities.

Lecture 10

Microscopic theory of ferromagnetism. Ising model. XY model. Heisenberg model.

Susceptibility above critical temperature. Correlation length.

Ornstein-Zernike correlation function. Paramagnons.

Lecture 11

Magnons in ferromagnets. Goldstone mode. Thermodynamics of FM. Bloch's law.

Lecture 12

Antiferromagnets. Excitations in AFM. Thermodynamics of AFM

Lecture 13

Spin dynamics. Bloch equation.

Lecture 14

Two types of relaxation processes in spin dynamics. Susceptibility tensor. Transverse relaxation.

Longitudinal relaxation. Macroscopic theory of spin waves.

Lecture 15

Kondo effect: experiment and theory. Indirect exchange: RKKY interaction

Lecture 16

Models of itinerant magnetism. Hubbard model. Anderson model. Stoner criterion.

Lecture 17

Strongly correlated systems 1: High-temperature superconductors. Mechanisms:

resonant valence bonds, paramagnons.

Lecture 18

Strongly correlated systems 2: Heavy fermions. Interplay between magnetism

and superconductivity.

Lecture 19

Effects of Coulomb interaction. Dynamical response functions. Dielectric function.

Coulomb screening. Plasmons.

Lecture 20

Disordered metals. Drude conductivity. Quantum correction to conductivity. Weak localization.

Zero-bias anomaly.

Lecture 21

Quantum fluctuations. Quantum criticality. Quantum phase transitions in strongly correlated systems.

Lecture 22

Nanostructures 1: Quantum dots. Coulomb blockade. Tunneling and co-tunneling.

Lecture 23

Nanostructures 2: Quantum wires. Breakdown of Fermi-liquid theory in 1D systems.

Luttinger liquids.

Lecture 24.

Nanostructures 3: Quantum transport through nanostructures.

Recommended literature:

1. N.W.Ashkroft and N.D. Mermin. Solid State Physics. (Holt, Rinehart and
Winston, New York 1976)

2. C.Kittel. Quantum Theory of Solids.(John Wiley and Sons, New York 1987)

3. J. M. Ziman. Principles of the Theory of Solids. (Cambridge University Press,
Cambridge, 1979)

4. A. Abrikosov. Fundamentals of the Theory of Metals (North-Holland,
Amsterdam, 1988)

5. R. White. Quantum Theory of Magnetism. (Springer-Verlag, 1983)

6. A. Auerbach. Interacting Electrons and Quantum Magnetism. (Springer-Verlag,
1994)

7. G.Mahan, Many-Particle Physics (Plenum press, NY 1993)