2020-03195 - Post-Doctoral Research Visit F/M Hamiltonian splitting for vectorial spin-Vlasov equations
Le descriptif de l’offre ci-dessous est en Anglais

Type de contrat : CDD

Niveau de diplôme exigé : Thèse ou équivalent

Fonction : Post-Doctorant

A propos du centre ou de la direction fonctionnelle

The Inria Rennes - Bretagne Atlantique Centre is one of Inria's eight centres and has more than thirty research teams. The Inria Center is a major and recognized player in the field of digital sciences. It is at the heart of a rich R&D and innovation ecosystem: highly innovative PMEs, large industrial groups, competitiveness clusters, research and higher education players, laboratories of excellence, technological research institute, etc.

Contexte et atouts du poste

Physical context
The interaction of a ultrafast electromagnetic pulse with the electronic spins in a ferromagnetic nanos-
tructure has been the object of intense investigations, both theoretical and experimental, over the past two
decades. The main e ect that was observed is the quick loss of magnetization following the excitation by the
laser pulse. Despite the fact that several mechanisms have been proposed to explain this demagnetization,
the scenario is far from being fully elucidated.
From a fundamental point of view, the modelling of a laser with electronic charges and spins represents
an ambitious theoretical and computational challenge, as it requires to include several e ects. In order to
tackle this complex problem which requires the modelling of nonlinear quantum-relativistic system of many
electrons, the IPCMS research group recently developed an original approach based on Wigner's phase-
space representation of quantum mechanics. In this formulation, the phase space distribution function is
not a scalar, but rather a 2 x 2 matrix, solution to a vectorial spin-Vlasov equation (coupled to Maxwell's
equations). This model constitutes a mean- eld semiclassical model where the electron orbital motion is
treated classically, while the spin is a fully quantum variable.

Mission confiée

For a better knowledge of the proposed research subject :
A state of the art, bibliography and scientific references, do not hesitate to contact the advisor. 


Collaboration :
The recruited person will be in connection with Nicolas Crouseilles and Pierre Navaro (Inria Rennes) and

in close collaboration with Giovanni Manfredi and Paul-Antoine Hervieux (IPCMS, Strasbourg). 

The candidate will benefit from a great scientific environment at the IRMAR laboratory https://irmar.univ-rennes1.fr 

Principales activités

Main objectives

The main goal of this postdoctoral project will be the numerical approximation and validation of this
spin-Vlasov model by means of Eulerian numerical methods (i.e. using a mesh of the phase space). As a
rst validation, the Vlasov models have been rst considered a simple slab geometry. However, to include
the Lorentz force (and hence the orbital magnetism and the spin-orbit coupling) a 4 dimensional phase space
has to be considered.
In this postdoctoral project, we will combine the expertise of the MINGuS team in terms of numerical
methods for Vlasov equations, namely semi-Lagrangian methods and Hamiltonian splitting. In particular,
this project will bene t from the SeLaLib library or Julia packages recently developed in the MINGuS team.
The postdoctoral fellow will be in charge of investigating, implementing and validating di erent numerical
methods for the spin-Vlasov models using Eulerian methods. The Hamiltonian structure of the system will
be of great importance to design a suitable time splitting which will be combined with high order methods
in phase space.


Technical skills and level required :

Languages : french, english 

Other valued appreciated : skills in numerical methods for PDEs, numerical analysis and scientific computing.  


Monthly gross salary amounting to 2130 euros