Syllabus
Programme:
1. Phonons in solids and theory of the Mössbauer effect - classical and quantum description of motion of nuclei, statistical properties of a system of linear harmonic oscillators, the Lamb-Mössbauer factor, relation to the Debye-Waller factor.
2. Groups and symmetry in solids - groups and their representations, reducible and irreducible representations, character of a representation, decomposition of a general representation into irreducible representations for a finite group, irreducible representations of space groups of solids, application of the group theory to the search and classification of eigenvalues of hamiltonians of atoms, molecules and solids.
3. 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.
4. 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.
5. 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, the Friedel oscillations, permittivity, the Thomas-Fermi screening, plasmons.
Annotation
The lecture represents a continuation of the lecture Physics of solids I (FPL143) and it is focused on selected equilibrium properties and collective phenomena, such as the Mössbauer effect, phase transitions in the Ising model, magnons in the Heisenberg model, screening and plasmons in an electron liquid. An introduction to the relevant theoretical tools is presented including fundamentals of the group theory.