Quantum dynamics: light and matter

Course given at IPCMS

course contents (18h):

EM Field: classical field theory and variational approach; Maxwell equations; Quantification of the electromagnetic fields.
Matter: Dirac equation; Spin and electron-positron solutions; Exact solution for the Coulomb potential; Quantification of the Dirac field.
Field + matter: QED; Light-matter interactions; Feynman diagrams; Description of simple processes: scattering of an electron by an external field, electron-electron scattering, Compton scattering, braking radiation, Kramers formula and Raman scattering, harmonic generation, Lamb shift; other non-linear scattering processes…
Low energy expansion of Dirac-Maxwell: Foldy–Wouthuysen transformation; One-, two- and many-electron systems; Mean-field approximation.
Nonlinear quantum dynamics: Wave-function-based methods: relativistic Hartree-Fock and DFT; Phase space methods: Wigner functions; Quantum hydrodynamics.
Quantum mechanics in the phase space: Wigner functions: negativity, entanglement; Wigner functions with spin: semi-relativistic effects, spin-orbit coupling; Beyond mean field: Wigner-Boltzmann equations and open quantum systems, decoherence; Applications: electron dynamics in thin metal films, spin corrections to plasmonic resonances.
Quantum Hydrodynamics (QHD): Madelung transformations and quantum hydrodynamics; QHD with spin: spin-orbit coupling and relativistic effects; Effect of the environment: quantum drift-diffusion models; Variational formulation; Applications: inverse Faraday effect.