- Basics of mathematical (computer) modelling for physicists
This undergraduate course describes basics of problem formulation, dependent and independent variables, internal/external parameters, phase space, linear and nonlinear systems, their description using 1-st order differential equations, equilibrium properties (fixed points), linearisation and stability problems, nonlinear systems with two degrees of freedom, spontaneous oscillations, Fourier analysis, correlations and noise, stochasticity and detour to probabilistic description, equations for probability density, appearance of master equation, Fokker-Planck equation, inter-relation between evolution of probability density and averaging over stochastic paths. The course ends with piece-wise deterministic processes.
- Applied thermodynamics
This undergraduate course describes basics of thermodynamics including the parametrisation, four laws, quasi-equilibrium processes, the closed and steady state processes, the essence of entropy, basic heat engine, Carnot cycle and the essence of efficiencies, thermodynamic potentials. Further on more realistic systems are described: gas power cycles, vapour power cycles, refrigeration cycles, problems of compressible flow, combustion, shock waves.
- Quantum relaxation theory
This graduate course extends the standard quantum mechanics. It develops formalism of stochasticity in open quantum problems by combining concepts from thermodynamics, statistical physics and quantum mechanics. It describes the density matrix approach, the real and imaginary time path integral approaches, Feynman-Vernon action principle. Additionally the variational approach of quantum physics is refreshed. Based on these several forms of the stochastic Schroedinger equation are obtained. Time dependent perturbation theory is developed for the general density matrix of an open quantum system. At the second order the Redfield equation is derived. Its utility is exemplified for the systems of harmonic oscillators, spin-boson problem, the electron-vibrational molecular systems and a system of coupled spins.
- Molecular physics and spectroscopy
This graduate course briefly describes physical problems of molecular systems, in particular the theoretical spectroscopy approach. The general response function theory is described. In order to apply it for molecular systems, the basic models of molecular systems are presented. These include a displaced oscillator model and the Frenkel exciton theory. In the rotating wave approximation the first and third order response functions for molecular systems are derived and visualised by the Feynman diagrams. Specific spectroscopy signals, e. g. absorption, fluorescence, pump-probe and the two-dimensional coherent spectroscopy are described.