Syllabus
* 7. Linear response function theory
General formalism, linear response function and sum rules, finite temperature, density response, current response, current response to an electromagnetic field, density response for non-interacting homogeneous systems;
* 8. Linear response function in different models
Linear response function in Landau theory, time-dependent Hartree (TDH) for homogeneous systems: RPA, TDH for the density matrix and the Landau equation, the RPA for electron gas in different dimensions: plasmon, the RPA for bosons, the time-dependent Hartree-Fock (TDHF) and the matrix RPAE, examples of application of the RPA theory (RPA with separanle interactions, RPAE for metal clusters), adiabatic time-dependent LSDA (TDLSDA) (the TDLSDA longitudinal response function, the TDLSDA transverse response function), TDLSDA commutators and symmetry restoration, the Kohn and Larmor theorems, magneto-conductivity and quantum Hall effects, linear response based on Green functions RPAE, screened response function and dielectric constant, examples of application of the TDLSDA theory (quantum wells under very high external magnetic field, quantum dots under magnetic field);
* 9. Dynamic correlations and response function
Interaction energy and correlation energy, the RPA correlation energy (for the cold and dilute gasses of boson and fermions), theories beyond the RPA, STLS theory, comparison of different theories for electron gas in 2D, quasiparticle properties, nonlocal effects, mean energy of many-particle excitations, the polarization potential model, the Gross-Kohn model, method of Lorentz transformations.
* 10. Hydrodynamic and elastic models
Hydrodynamic model of bosons (backflow compensation and surface modes of spherical drops, comparison and surface modes of Bose gas in a magnetic trap, moment of inertia and the scissor mode of a Bose gas in a magnetic trap);
Fluidodynamic and hydrodynamic models for fermions (dipolar modes in metal clusters, the scalar quadrupole mode in confined systems, the scissor mode in Fermi systems, the moment of inertia of quantum dots, the vibrating potential model);
Surface vibrations of charged systems in 2D and 3D (surface vibrations of charged metal clusters, edge vibrations of quantum dots ).
Annotation
teorie lineární odezvy, funkce lineární odezvy v různých modelech (TDHF, RPA, Kohn-Larmorův teorém, kvantový Hallův jev, kvantové body v magnetickém poli, kvantové jámy v magnetických polích), dynamické korelace a funkce odezvy
(RPA korelace ve studeném bosonovém a fermionovém plynu, elektronový dvourozměrný a třírozměrný plyn, Gross-Kohnův model), hydrodynamické a elastické modely bosonových a fermionových plynů (dipolové, kvadrupolové, nůžkové excitace v kvantových bodech a metalických klastrech) .
Tato přednáška navazuje na přednášku NJSF132.