COURSE GOALS: The principle objective of the course Quantum statistical physics is to learn
new methods in solving many body quantum-mechanical problems. This methods
are second quantization, many body perturbation theory (Feynman's diagrams), linear response theory and mean field methods such as Local Density Approximation (LDA).
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
Upon completing the degree, students will be able to:
1. KNOWLEDGE AND UNDERSTANDING
1.2 demonstrate a thorough knowledge of advanced methods of theoretical physics including classical mechanics, classical electrodynamics, statistical physics and quantum physics
1.3 demonstrate a thorough knowledge of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena)
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.2 evaluate clearly the orders of magnitude in situations which are physically different, but show analogies, thus allowing the use of known solutions in new problems;
2.3 apply standard methods of mathematical physics, in particular mathematical analysis and linear algebra and corresponding numerical methods
3. MAKING JUDGEMENTS
3.2 develop a personal sense of responsibility, given the free choice of elective/optional courses
4. COMMUNICATION SKILLS
4.3 develop the written and oral English language communication skills that are essential for pursuing a career in physics
5. LEARNING SKILLS
5.1 search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development (good knowledge of technical English is required)
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon passing the course Quantum statistical physics the student will be able to:
1.understand how to utilize the second quantization in solving quantum mechanical problems,
2.recognize the advantage of using propagators or Greens functions in solving quantum mechanical problems which includes many bodies in interaction.
3.use many body perturbation theory methods which includes diagrammatic approach,
4.understand the linear response theory, to construct the response function of interacting electron gas, of atom, or of molecules.
5.understand mean filed theories such as Density Functional Theory (DFT).
COURSE DESCRIPTION:
1. Transition from first to second quantization
2. One and two particle operators in second quantization
3. Fermion's and boson's Green's functions
4. Many body perturbation theory
5. Wick's theorem, connected, disconnected, irreducible diagrams
6. Harteree-Fock approximation and correlation energy in degenerated electron gas
7. Linear response theory (Kubo formula)
8. Response function of degenerated electron gas (Linhard function)
9. Random Phase Approximations (RPA) in degenerated electron gas
10. Statical, dynamical (collective excitations) and long weave length (Thomas-
Fermi) approximations
11. Density Functional Theory (DFT)
12. DFT approximations: Local Density approximation (LDA), Generalized Gradient Approximation (GGA)
13. Quasi-particle GW approximation.
REQUIREMENTS FOR STUDENTS:
Students should attend lectures and exercises and solve one rather difficult problem which requires numerical calculations.
GRADING AND ASSESSING THE WORK OF STUDENTS:
The final grade is formed from the seminar paper (2 ECTS) and the final oral exam (3 ECTS).
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- T.D. Schultz: Quantum Field Theory and the Many-Body Problem, Gordon and Breach,
New York, 1963
- A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinskii: Methods of Quantum Field Theory in
Statistical Physics, Prentice-Hall, Englewood Cliffs, 1963
- A Mattuck: Guide to Feynman Diagrams in the Many-Body Problem, New York, 1967
- A. Fetter-J. D. Walecka: Quantum Theory of Many-Particle Systems, McGraw Hill, New
York, 1971
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