| Individual course details | ||||||||||
| Study programme | Theoretical and experimental physics | |||||||||
| Chosen research area (module) | ||||||||||
| Nature and level of studies | Basic academic studies | |||||||||
| Name of the course | Quantum statistical physics | |||||||||
| Professor (lectures) | Full Professor Zoran Radović / Doc. dr Mihajlo Vanević | |||||||||
| Professor/associate (examples/practical) | ||||||||||
| Professor/associate (additional) | ||||||||||
| ECTS | 6 | Status (required/elective) | elective | |||||||
| Access requirements | Statistical physics 1 and 2, Quantum mechanics 1 | |||||||||
| Aims of the course | Introduction to modern methods of quantum statistical physics | |||||||||
| Learning outcomes | Mastering modern methods of quantum statistical physics | |||||||||
| Contents of the course | ||||||||||
| Lectures | 1.
Representation of second quantization: Quantum mechanics of identical
particles, bosons and fermions. Representation of second quantization for
single-particle and two-particle operators. Field operators in the Heisenberg
representation, equation of evolution. 2. Statistical operator: Definition and properties. Method of statistical ensembles for thermal equilibrium. Bloch's diagonalization of the statistical operator for harmonic oscillators. Statistical physics of ideal Bose and Fermi gases. 3. Superfluid phenomenon: Energy spectrum of interacting bosons at low temperatures. Effective Hamiltonian. Bogoliubov canonical transformations and hamiltonian diagonalization. Phonons and rotons. Landau criteria for superfluidity. Quantization of angular momentum. Superfluidity of He4. 4. Variational and perturbation techniques: Wick's theorem. Hartree-Fock variational method. Determination of the ground state of interacting fermions. Feynman's diagrammatic technique. Dyson equation. Hartree-Fock approximation and RPA in diagrammatic technique. Application to the Fermi liquid. Plasma oscillations. Electron-phonon interaction. 5. Superconductivity - basic experimental facts. Cooper's problem. Bardeen-Cooper-Schrieffer (BCS) model hamiltonian and variational trial function. Solution of the self-consistent equation near the critical temperature. BCS equation for the critical temperature (explanation of isotopic effect). 6. Magnetism: Quantum nature of magnetism - Bohr-van Loeven theorem. Heitler-London theory of hydrogen molecules. Exchange interaction. Heisenberg model: Ground state and spin waves. Magnons and Bloch's law T^3/2. Mean-field approximation. Ising's model. 7. Introduction to quantum kinetic theory: Fluctuation-dissipation theorem. Cubo's theory of the linear response. |
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| Examples/ practical classes | Problem solving classes | |||||||||
| Recommended books | ||||||||||
| 1 | E.M. Lifshitz & L.P. Pitaevskii, Statistical Physics, Part 2: Vol. 9 (Butterworth-Heinemann, 1980). | |||||||||
| 2 | E.M. Lifshitz & L.D. Landau, Statistical Physics, Part 1: Vol. 5 (Butterworth-Heinemann, 1980). | |||||||||
| 3 | L.D. Landau & E.M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Vol. 3 (Pergamon Press, 1977). | |||||||||
| 4 | M. Tinkham, Introduction to Superconductivity (McGraw-Hill, 1996). | |||||||||
| 5 | ||||||||||
| Number of classes (weekly) | ||||||||||
| Lectures | Examples&practicals | Student project | Additional | |||||||
| 4 | 2 | |||||||||
| Teaching and learning methods | Lectures, problem solving classes, consultations, homework assignments | |||||||||
| Assessment (maximal 100) | ||||||||||
| assesed coursework | mark | examination | mark | |||||||
| coursework | 10 | written examination | 40 | |||||||
| practicals | oral examination | 40 | ||||||||
| papers | 10 | |||||||||
| presentations | ||||||||||