# Theoretical Condensed Matter Physics

### Theoretical Condensed Matter Physics

 Code: 205311 ECTS: 0.0 Lecturers in charge: dr. sc. Osor Slaven Barišić - Lectures Take exam: Studomat

### 1. komponenta

Lecture typeTotal
Lectures 36
Exercises 18
Description:
Field theoretical methods in solid state physics: Many body systems, exact and approximate methods. Green's functions - propagators. Definitions, properties. Perturbation method, Feynman diagrams. Vacuum fluctuations, connected and disconnected diagrams. Linked Cluster Theorem. Particle self-energy, Dyson equation. Quasiparticle - definition and properties. Ground state energy: Coulomb (Hartree) and exchange (Fock) energies, correlation energy; Equation of motion for the Green's function, solution methods (Hartree, Hartree-Fock); Boson Green's functions; Fermion-boson interaction; Polaron, renormalization of particle mass and energy
Linear response theory: Correlation functions and the differential cross section. Dynamical and static structure factors; Neutron and x-ray scattering in crystals: differential cross section, elastic scattering, Debye-Waller factor, phonon emission and absorption; Response functions ; Kubo formula, spectral representation; Properties of response functions, connection with correlation functions; Free fermion response function (Lindhard);Static and dynamic limits, Kohn anomaly and Friedel oscillations;Boson response function;Current-current response function. Conductivity. Optical properties.
Collective phenomena in the Coulomb gas: Dynamically screened Coulomb interaction. Random Phase Approximation (RPA); Excitation spectrum, plasmons in the electron gas. Landau damping; Dynamical and static longwavelength limits. Thomas-Fermi screening; Connection with the dielectric function; GW approximation, ground state energy
Electron states in condensed matter : Localized state spectra; Nonperturbative calculation, cumulant expansion, Independent Boson Model (IBM); Properties of the spectra: ground state energy shift, satellites, sum rules, Koopmans theorem; Adiabatic and sudden transitions, effects on relaxation and screening; Examples: electron-phonon and electron- electron interaction, discrete and continuous excitations; Electronic state decay, irreversibility, Fano-Anderson model; Delocalized state spectra; Radiation absorption spectra
Density functional theory: Kohn-Hohenberg theorem, ground state energy as the density functional; Self-consistent Kohn-Sham equations; Local density approximation (LDA), Approximations for the exchange and correlation energy; Examples, discussion of the results
Density matrices: Definitions and properties. Natural orbitals; Hartree-Fock approximation; Free fermions - Fermi hole; Pair distribution function and the static structure factor
Literature:
1. A.P.Abrikosov, J.I.Gorkov, I.E. Dyaloshinskii, Methods of Quantum Field Theory in Statistical Physics, (new ed.), Dover 1976
2. A.L.Fetter-J.D.Walecka: Quantum Theory of Many-Particle Systems, McGraw Hill, New York, 2003
3. M. Šunjić: Kvantna fizika mnoštva čestica, (Školska knjiga, Zagreb, 2002)
4. G.D.Mahan: Many-Particle Physics, Plenum, 1990
 1. semester Fizika kondezirane tvari - redovni predmeti - Mandatory smjer - Condensed matter physics
Consultations schedule: