Syllabus
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).
Annotation
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.