Quantum dynamics: light and matter

Description

  This course provides a general overview of the theoretical and numerical methods used to describe the electronic dynamics in nanoscale metal objects. Magnetic effects (spin) will also be taken into consideration. General information on metallic nano-objects, space scales, time and energy, coupling parameters.

Compétences visées

The student will learn to use and manipulate the theoretical tools commonly used to describe electronic transport in metallic nano-objects. The student will also learn to implement these methods in numeric codes. These skills can be transferred to other areas of physics, including the physics of gases and plasmas.
At the end of this course the student will be able to understand and model the dynamics of the charges and spins in different nano-objects that he will meet in his later course. He will have an overview of the theoretical methods used in this field and may also consider the numerical modeling of these nano-objects. The theoretical tools acquired will be essential not only for the study of nanosciences, but also for all the physics of condensed matter.
Version française

L’étudiant apprendra à utiliser et manipuler les outils théoriques couramment utilisés pour décrire le transport électronique dans les nano-objets métalliques. L’étudiant apprendra également à implémenter ces méthodes dans des codes numériques. Ces compétences peuvent être transposées à d’autres domaines de la physique, notammment la physique des gaz et des plasmas.

A l’issue de ce cours l’étudiant sera capable de comprendre et modéliser la dynamique des charges et des spins dans différents nano-objets qu’il rencontrera dans son cursus ultérieur. Il aura une vision d’ensemble des méthodes théoriques utilisées dans ce domaine et pourra également envisager la modélisation numérique de ces nano-objets. Les outils théoriques acquis constitueront un bagage essentiel non seulement pour l’étude des nanosciences, mais également pour toute la physique de la matière condensée.

Syllabus

• 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.

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