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Reference : UMR5493-NICROU-003
Workplace : GRENOBLE
Date of publication : Wednesday, July 29, 2020
Scientific Responsible name : Nicolas Rougerie
Type of Contract : PhD Student contract / Thesis offer
Contract Period : 36 months
Start date of the thesis : 1 October 2020
Proportion of work : Full time
Remuneration : 2 135,00 € gross monthly
Description of the thesis topic
Mathematical Physics research on the quantum many-body problem. More precisely, the mean-field limit for of fermions in a large magnetic field.
``Mean-field limit'' refers to the process leading from a fundamental model of interacting particles (linear most of the time) to an effective model (non-linear) for the evolution of a single typical particle. The mathematical study of quantum mean-field limits has made a lot of progress in the past twenty years. This internship topic is part of this general effort.
We propose to study the mean-field limit of the ground state of a system of confined fermions (particles satisfying the Pauli exclusion principle) under a strong magnetic field, taking inspiration from the recent works of Fournais-Lewin-Solovej and Fournais-Madsen.
Two cases that have not been treated so far could be of interest to us : strong magnetic field limit in a fixed box, and strong magnetic field limit with inhomogeneous magnetic field. In both cases, one must study a joint mean-field/semi-classical limit, and acquaint oneself with the appropriate mathematical tools.
The work will take place at "Laboratoire de Physique et Modélisation des Milieux Condensés" et est financé par la bourse ERC "Correlated frontiers of many-body quantum mathematics and condensed matter physics".
The LPMMC is a joint research unit in physics regrouping diverse theoretical competences under supervision of the Université Joseph Fourier (UJF) and of the Centre National de la Recherche Scientifique (CNRS). The laboratory was first dedicated to numerical physics, it is now mainly oriented towards condensed matter and quantum physics.
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