Infopaket

Theory of many-particle systems

ОК 6

Обов’язкова дисципліна для ОП

Second

2023/2024

1 Semester

3

Know the basic concepts of the theory of Bose-Einstein condensation and quantum fluids. Know the basic methods of calculating the statistical characteristics of Bose-Einstein condensates of ultracold gases. Know the basic research methods of microscopic theory of superfluidity. Be able to apply approximate methods in the theory of systems of many particles. Be able to apply the method of secondary quantization to solve practical problems in the physics of ultracold atomic gases. Be able to obtain numerical solutions of the Gross-Pitaevsky equation.

Full-time form

1. Know the basic principles of quantum mechanics, electrodynamics and statistical physics. 2. Be able to solve problems in the theory of systems of many particles, use a chart technique and find Green 's functions of quantum systems with whole spin, plan your own work and evaluate its results and consequences. 3. Have the skills to search and study specialized literature, solving algebraic and differential equations, work with interactive and multimedia tools.

Topic 1 Distributions of Bose-Einstein and Fermi-Dirac. Topic 2 Thermodynamics of an ideal gas. Topic 3 Gross-Pitaevsky equation. Topic 4 Systems with finite number of particles. Topic 5 Spinor condensates. Topic 6 Quantum field perturbation theory for superfluid helium. Topic 7 Landau superfluidity criterion. Topic 8 Methods of renormalization in field perturbation theory.

1. Вакарчук І.О. Квантова механіка. Львів: Львівський національний університет імені Івана Франка, 2012. – 872 с. 2. Landau L.D., Lifshitz E.M. Course of Theoretical Physics. V.5 Statistical physics. Part 1. – 3rd ed. Oxford: Butterworth-Heinemann, 1980. – 497 p. 3. Bose–Einstein Condensation / Ed. by A. Griffin, D. W. Snoke, S. Stringari. Cambridge: Cambridge University Press, 1995. – 602 p. 4. Ровенчак А. 80 років історії досліджень Бозе-Систем / Світ фізики. – 2004. - №3(27). С. 3-9. 5. M. H. Anderson, J. R. Ensher, M. R. Matthews et al. Observation of Bose–Einstein condensation in a dilute atomic vapor // Science. 1995. Vol. 269, no. 5221.P. 198–201. 6. Tisza L. The theory of liquid helium. // Phys. Rev.1947. Vol. 72, no. 9. P. 838–854. 7. V. Bagnato, D. Kleppner. Bose–Einstein condensation in low-dimensional traps // Phys. Rev. A. 1991. Vol. 44. P. 7439–7441.

Lectures, practical classes, independent work.

Modular tests, control of practical tasks, oral examinations, final test.

Ukrainian