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Course, academic year 2022/2023
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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
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. Mgr. František Šanda, Ph.D.
doc. RNDr. Miroslav Pospíšil, Ph.D.
Annotation -
Last update: prof. RNDr. Marek Procházka, Ph.D. (28.04.2020)
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.
Course completion requirements -
Last update: doc. Mgr. František Šanda, Ph.D. (30.04.2020)

Oral exam after written preparation

Literature -
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.

Requirements to the exam - Czech
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.

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

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.

Molecules in optical fields: Bloch equations. Absoption line shapes. Bayesian quantum statistics. Photon arrival trajectories. Dynamical spectroscopy.

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