Mathematical modelling combined with numerical simulation with application to quantum physics

A 1 year PostDoc position is available in the framework of the ANR LODIQUAS (Modeling and Numerical Simulation of Low Dimensional Quantum Systems, 2012-2015) at the IMT/MIP laboratory, Toulouse.

This ANR-project is dedicated to the mathematical modelling and numerical simulation of stationary and time dependent NonLinear Schroedinger equations (NLS) for quantum mechanical systems that are confined in one or more space dimensions. Such systems, like the 2DEG (2 dimensional electron gas) or 1DBEC (one dimensional Bose Einstein Condensates) are interesting both from the theoretical point of view and for applications like quantum semi-conductors or atom-chips.

The confinement of the quantum particle gas in one, two ("quantum wires") or even 3 space dimensions ("quantum dots") leads to some model reductions, which are very interesting (and challenging at the same time) from a numerical point of view. The confinement can be described by adding in the Hamilton operator a confining potential with a small parameter, e.g. an anisotropic harmonic oscillator potential or homogeneous Dirichlet boundary conditions in some direction(s). The vanishing parameter limit then yields an asymptotic model, which reduces considerable the computional time. The aim of this PostDoc position shall be the development, the mathematical analysis, the implementation and the testing of so-called Asymptotic-Preserving methods in the context of a confined quantum electron gas in a semiconductor device.

Required skills: Mathematical, numerical and computational knowledge. Some physical foundations in quantum physics.

Contact: Please sent a CV to the scientific advisors Claudia Negulescu,

e-mail: claudia.negulescu@math.univ-toulouse.fr

and Fanny Delebecque,

e-mail: fanny.delebecque@math.univ-toulouse.fr