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Course, academic year 2023/2024
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Classical and quantum statistical physics of molecular systems - NBCM160
Title: Klasická a kvantová statistická fyzika molekulárních systémů
Guaranteed by: Institute of Physics of Charles University (32-FUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020
Semester: winter
E-Credits: 4
Hours per week, examination: winter s.:3/0, Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Guarantor: doc. Mgr. František Šanda, Ph.D.
doc. RNDr. Miroslav Pospíšil, Ph.D.
Annotation -
Introduction to the study of molecular systems by methods of classical and quantum statistical physics. The lecture aims to establish a solid foundations for the use of molecular dynamics and to introduce to the density matrix - the central concept of quantum statistics with the perspective to model electronic and vibrational coherence. Thorough understanding of quantum-classical correspondence will be emphasized.
Last update: Procházka Marek, prof. RNDr., Ph.D. (28.04.2020)
Course completion requirements -

Oral exam after written preparation

Last update: Šanda František, doc. Mgr., Ph.D. (30.04.2020)
Literature -

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.

Last update: Šanda František, doc. Mgr., Ph.D. (03.03.2023)
Requirements to the exam - Czech

Požadavky u ústní zkoušky odpovídají sylabu předmětu v rozsahu, který byl prezentován na přednášce.

Last update: Šanda František, doc. Mgr., Ph.D. (03.03.2023)
Syllabus -

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.

Last update: Šanda František, doc. Mgr., Ph.D. (26.04.2023)
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