UE Modeling in nanosciences

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Degrees incorporating this pedagocial element :


Scaling devices down the nanoscale allows generating new physical properties and functionalities thanks to the discretization of electronic and/or photonic density of states.  Modeling the physics at this intermediate scale between atoms and macroscopic world is therefore a prerequisite as it strongly deviates from that of bulk material: size, shape, composition and environment are as many parameters which have to be controlled in order to taylor their properties. The aim of the course is therefore to introduce concepts, methods and tools required to simulate the physical properties of nanoscopic systems and to describe their coupling to the environment. The course will be illustrated by examples in optics, transport, mechanics and magnetism and numerical simulations.

The course will address three main subjects:

  • Electronic properties of nanoscopic systems in the single electron approximation: band structures of 2D layered materials, quantum confinement in semiconductors, quantum transport. It will be based on LCAO methods and effective Schrödinger equation.
  • Finite elements methods for partial derivative equations applied to nanomechanics, microfluidics, nanophotonics and nanomagnetism. The main concepts will be illustrated by examples of numerical simulations with Comsol sofware.
  • Dynamics of quantum systems: The density matrix and master equation formalism will be introduced and applied to quantum optics, nanomechanics and spin dynamics.

Recommended prerequisite

quantum physics, solid state physics, semiconductor physics, electromagnetism, partial derivative equations.