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Course, academic year 2023/2024
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Methods of Statistical Physics - NFPL088
Title: Metody statistické fyziky
Guaranteed by: Department of Condensed Matter Physics (32-KFKL)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: winter
E-Credits: 3
Hours per week, examination: winter s.:2/1, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: English
Teaching methods: full-time
Teaching methods: full-time
Guarantor: Ing. Richard Korytár, Ph.D.
doc. RNDr. Karel Carva, Ph.D.
Artur Slobodeniuk, Ph.D.
Classification: Physics > Solid State Physics
Files Comments Added by
download t_bc_ol_201005.pdf Basic concepts and relations of statistical physics doc. RNDr. Ilja Turek, DrSc.
download t_mf_ol_201023.pdf Mean-field approximation for Ising model doc. RNDr. Ilja Turek, DrSc.
download t_sp_ol_201110.pdf Screening and plasmons in homogeneous electron liquid doc. RNDr. Ilja Turek, DrSc.
Annotation -
Last update: RNDr. Mgr. Michal Turek (06.02.2007)
The lecture represents a continuation of the basic course of statistical physics (OFY031) and it is focused on properties of the condensed state. It starts with a brief review of standard chapters followed by the theory of selected equilibrium properties (the Ising model, magnons, electron liquid, the Bose-Einstein condensation) including an introduction of the relevant theoretical methods. In the end, the Boltzmann kinetic equation is mentioned as a tool for treatment of non-equilibrium properties. The lecture is in English. For post-graduate students.
Course completion requirements -
Last update: Ing. Richard Korytár, Ph.D. (12.05.2022)

The course is completed with an oral exam.

Credit is granted if the student participates actively in the Problem Classes and presents successful solutions to a given number of problems, specified at the beginning of the semester.

Requirements to the exam - Czech
Last update: doc. RNDr. Ilja Turek, DrSc. (12.10.2017)

Zkouška má pouze ústní část. Požadované znalosti odpovídají sylabu předmětu v rozsahu prezentovaném na přednášce.

Syllabus -
Last update: RNDr. Mgr. Michal Turek (06.02.2007)

Programme:

1. Fundamentals of the classical and quantum statistical physics - thermodynamic equilibrium, ergodicity, distribution functions, linear harmonic oscillator, systems of identical non-interacting particles.

2. Mean-field approximation for the classical Ising model - the Peierls-Feynman inequality, the Ising model of magnetism, molecular field, ferromagnetism, critical behavior, the Landau theory, complex magnetic orders, order-disorder transitions in substitutional solid solutions.

3. Magnons in the quantum Heisenberg model - correlation functions and their spectral representations, equations of motion and their approximative solution, local and collective spin excitations, renormalized magnons, critical behavior, the Bloch law.

4. Screening and plasmons in an electron liquid - the Kubo linear response theory, fluctuation-dissipation theorem, pair (particle-hole) excitations in non-interacting systems, dynamical response of a homogeneous non-interacting electron gas and of an interacting electron liquid in the Hartree approximation, permittivity, the Thomas-Fermi screening, plasmons.

5. The Bose-Einstein condensation - its appearance in homogeneous non-interacting systems, inclusion of a weak interaction within the Hartree approximation, the Gross-Pitaevskii equation, condensation in atomic traps, off-diagonal long-range order.

6. Non-equilibrium properties of many-particle systems - the Boltzmann equation for atoms in gases and for electrons in solids, transport phenomena in metals.

Literature:

1. J. Kvasnica: Statistická fyzika (Academia, 1983).

2. R. P. Feynman: Statistical mechanics (W. A. Benjamin, 1972).

3. M. Toda: Statistical Physics I (Springer, 1998); R. Kubo: Statistical Physics II (Springer, 1998).

4. S. V. Tjablikov: Metody kvantovoj teorii magnetisma (Nauka, 1975).

5. N. N. Bogoljubov: Vvedenije v kvantovuju statističeskuju mechaniku (Nauka, 1984).

6. R. Kužel: Úvod do fyziky kovů II (SNTL, 1985).

 
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