TFNSP0004 Statistical Physics and Kinetic

Institute of physics in Opava
summer 2024
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Martin Blaschke, Ph.D. (lecturer)
RNDr. Martin Blaschke, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Martin Blaschke, Ph.D.
Institute of physics in Opava
Timetable
Tue 10:35–12:10 B4
  • Timetable of Seminar Groups:
TFNSP0004/A: Wed 8:55–10:30 309, M. Blaschke
Prerequisites
(FAKULTA(FU) && TYP_STUDIA(N))
Basic knowledge of thermodynamics. Basic knowledge of mathematical analysis, e.g. the method of Lagranger multipliers, Striling's formula, Gauss's integral. Basic knowledge of matrix algebra up to Jordan normal matrix form.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course enables students to get acquainted with the basic methods of statistical physics and kinetics. It follows the equilibrium thermodynamics and expands the issue of phase transitions, where the student gets acquainted with critical points and so-called critical phenomena on the Ising model of ferromagnetism.
Learning outcomes
After completing the course, the student will be able to: -solve basic problems of statistical physics using the partition function. -derive various classical and quantum distributions. -solve Ising's model accurately and using the field wiping method.
Syllabus
  • The main topics of the course are:
    • Phase volume, Equilibrium definition, Fluctuations, Ensambles definition, Ergodic problem, Liouville's theorem
    • Microcanonic ensemble, partition sum, equation of state of an ideal gas
    • Canonical ensemble, equation of state of an ideal gas
    • Principle of maximum entropy, Boltzmann construction
    • Grandcanonical ensemble, equation of state of an ideal gas, two atomic gas, interactions
    • Ursell-Mayer development and Mayer's theorem, van der Waals equation of state, surface tension and Laplace pressure
    • Phase transitions, classification of phase transitions and Ehrenfest equations, mechanism of new phase formation, critical point
    • Clasiuos – Claipeyron equation, Gibbs phase rule, Fluctuation, Generalized Redlich – Kwong equation of state
    • Ising's model of ferromagnetism, Mean field theory
    • Critical exponents
    • Fluctuations, stochastic processes and kinetic equations. Fluctuations of thermodynamic quantities; thermodynamical nonequilibrium systems; stochastic forces; Fokker-Planck equation; basic equations of kinetics; • Boltzmann's kinetic equation; transport equations; the law of growth of Boltzmann entropy; spontaneous transition of the system to equilibrium; irreversible processes; locally equilibrium systems; linear thermodynamics; Onsager relations.
    • Non-equilibrium systems. Statistical operator; linear system reactions; plasma and plasma effects; zero sound in the fermion system; fluctuation-dissipation theorem; dispersion relations; Green's functions.
Literature
    recommended literature
  • Tong, D. Kinetic Theory, lecture notes, University of Cambridge, http://www.damtp.cam.ac.uk/user/tong/kinetic.html, 2012
  • Jaynes, E. T. Probability Theory As Extended Logic, https://bayes.wustl.edu/, 1950-2003
  • Kvasnica, J. Statistická fyzika. Academia, Praha, 1998. ISBN 80-200-0676-1. info
  • Atkins, P., de Paula, L. Fyzikální chemie. Praha, 2013. ISBN 978-80-7080-830-6. info
  • Reif F. Fundamentals of Statistical and Thermal Physics. McGraw-Hill, 1965. info
Teaching methods
Lectures, homeworks
Assessment methods
oral examination, written test
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms summer 2021, summer 2022, summer 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.slu.cz/course/fu/summer2024/TFNSP0004