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Last update: prof. RNDr. Marek Procházka, Ph.D. (28.04.2020)
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Last update: doc. Mgr. František Šanda, Ph.D. (30.04.2020)
Oral exam after written preparation |
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Last update: doc. Mgr. František Šanda, Ph.D. (03.03.2023)
Tuckerman, Mark. Statistical Mechanics: Theory and Molecular Simulation, OUP Oxford, 2010. Steinhauser, Martin Oliver. Computer simulation in physics and engineering, De Gruyter, Berlin, 2013. Šanda, František. Quantum statistical physics of molecular systems, Lecture Notes, Praha, 2022. |
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Last update: doc. Mgr. František Šanda, Ph.D. (03.03.2023)
Požadavky u ústní zkoušky odpovídají sylabu předmětu v rozsahu, který byl prezentován na přednášce. |
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Last update: doc. Mgr. František Šanda, Ph.D. (26.04.2023)
Mechanics of molecular systems. Statistical ensembles, random walks, discrete and continuous probability, maximal likelihood principle, temperature. Liouville theorem and Liouville equation. Introduction to molecular dynamics, microcanonical ensemble, classical virial theorem, thermal equilibrium. Integration of equations of motion: finite difference methods, classical operator of time evolution and numerical integrators. Classical time-dependent statistical mechanics and linear response theory. Quantum models in biophysics and chemical physics: Nuclear spins. Molecular vibrations. Electronic states. Density matrices: Populations and coherences. Wave function collapse. Liouville-von Neumann equation. Quantum-classical mapping: Bloch sphere. Wigner density. Bohr-Sommerfeld quantization. Quantum statistics at equilibrium: Canonical density matrices. Boson condensation. Gibbs paradox. Fermi-Dirac and Bose-Einstein distributions. Quasiparticles. Emergence of relaxation: von Neumann entropy. Unitary evolution. Reduced density matrix. Random Hamiltonian. Decoherence. Liouville space, superoperators. Quantum master equations: Quantum semigroups, Lindblad form, Stochastic Liouville equations, Open quantum systems. Secular dynamics. Thermodynamics of quantum relaxation. Molecules in optical fields: Bloch equations. Absoption line shapes. Bayesian quantum statistics. Photon arrival trajectories. Dynamical spectroscopy. |