Mihajlo Vanevic photo

Dr. Mihajlo Vanević

Condensed Matter Theory Group

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Quantum Statistical Physics

Teaching assistant:

Course is offered in the winter semester to the 4th year students with the major
in Theoretical and Experimental Physics.

Course program and suggested reading:

1. Second quantization: Identical particles. Bosons and fermions. Second quantization of single- and two-particle operators. Field operators. Evolution in the Heisenberg picture.

   [F] Ch. 6, especially §7, §8; §9*, §10*. See also [BF] Ch. 1

2. Statistical operators: Definition and properties. Statistical ensembles for the systems in equilibrium. Bloch calculation of the diagonal elements of the statistical operator for the linear harmonic oscillator. Ideal Bose and Fermi gases.

   [F] Ch.2 §1-5 (see also [L3] §14 and [L5] §8); [L5] §30, p1; [L5] §56-59, §60*, §61*, §62, p1, §63

3. Superfluidity: Energy spectrum of the weakly interacting bosons at low temperature. Effective Hamiltonian. Diagonalization by Bogoliubov canonical transformations. Phonons and rotons. Landau criterion for superfluidity. Quantization of the angular momentum. Superfluidity of 4He.

   [L9] §22, §23, §25, §26, §29, p1, p2, §30*. See also [F] Ch. 11

4. Variational and perturbational techniques: Wick's theorem. Hartree-Fock method for the ground state energy of the system of interacting fermions. Feynman diagrammatic technique. Dyson equations. Hartree-Fock and random phase approximations in the diagrammatic technique. Fermi liquids. Plasma oscillations. Electron-phonon interaction.

5. Superconductivity: Experiments and phenomenology. Cooper pairing. Bardeen-Cooper-Schrieffer (BCS) model Hamiltonian. Diagonalization by Bogoliubov transformations. Order parameter in the vicinity of Tc. BCS equation for Tc. Isotope effect.

   [T] §1.1, §1.2, §1.4, §1.5*, §1.7, §2.1, §2.2; Ch. 3 §3.1, §3.2*, §3.3-3.6, §3.7.1, §4.5. See also [F] Ch. 10

6. Magnetism: Quantum nature of magnetism. Bohr-van Leeuwen theorem. Heitler-London theory of the hydrogen molecule. Exchange interaction. Heisenberg model: ground state and spin waves. Magnons and Bloch's T3/2 law. Mean field approximation. Ising model.

7. Introduction to quantum kinetic theory. Fluctuation-dissipation theorem. Kubo linear response theory.

   [L5] §123, §124, §126*; [BF] Ch. 6 §6.1


[F]R. Feynman, Statistical Mechanics (1972)
[Lx]L. Landau and E. Lifshitz, Course of Theoretical Physics, Vol. x (~1980)
[T]M. Tinkham, Introduction to Superconductivity (McGraw-Hill, 1996)
[BF]H. Bruus and K. Flensberg, Many-body quantum theory in condensed matter physics: an introduction (2004)