Dr. Mihajlo Vanević
Condensed Matter Theory Group

email: tel: +381 11 7158 154 or ~169 fax: +381 11 3282 619 office: 650 or 757 address: Department of Physics, University of Belgrade
Studentski trg 12, 11158 Belgrade, Serbia
Quantum Statistical Physics
Lectures:  
Exercises: 
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 twoparticle 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 §15 (see also [L3] §14 and [L5] §8); [L5] §30, p1; [L5] §5659, §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 ^{4}He.
[L9] §22, §23, §25, §26, §29, p1, p2, §30*. See also [F] Ch. 11
4. Variational and perturbational techniques: Wick's theorem. HartreeFock method for the ground state energy of the system of interacting fermions. Feynman diagrammatic technique. Dyson equations. HartreeFock and random phase approximations in the diagrammatic technique. Fermi liquids. Plasma oscillations. Electronphonon interaction.
5. Superconductivity: Experiments and phenomenology. Cooper pairing. BardeenCooperSchrieffer (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*, §3.33.6, §3.7.1, §4.5. See also [F] Ch. 10
6. Magnetism: Quantum nature of magnetism. Bohrvan Leeuwen theorem. HeitlerLondon theory of the hydrogen molecule. Exchange interaction. Heisenberg model: ground state and spin waves. Magnons and Bloch's T^{3/2} law. Mean field approximation. Ising model.
7. Introduction to quantum kinetic theory. Fluctuationdissipation theorem. Kubo linear response theory.
[L5] §123, §124, §126*; [BF] Ch. 6 §6.1
Literature:
[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 (McGrawHill, 1996)
[BF]H. Bruus and K. Flensberg, Manybody quantum theory in condensed matter physics: an introduction (2004)