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# Quantum Dynamics and Spectral Analysis

contact : contact-QDSA@cpt.univ-mrs.fr

Spectral and scattering theory

Quantum wave guides

Boltzmann equations

Quantum field theory

Inverse problems

The research of the team Quantum Dynamics and Spectral Analysis is focused on development of mathematical methods for applications to problems in physics. In particular, our research pertains to diffusion and spectral properties of nanostructure models, of models in atomic physics or in quantum field theory, properties of the solutions of partial differential equations that occurs in physics, and unicity, stability and reconstruction in inverse problems.

Our main scientific activities are:

Nanostructures: Scattering properties of waves in optic fibres and in quantum wave guides; spectral properties of differential operators on graphs; gap opening at Fermi level and semiconductivity via periodic electrostatic gating in graphene samples ; Andreev reflection for SNS junctions in semiclassical limit.

PDE and inverse problems: Inverse problems for anomalous diffusion of time fractional equations of complex fluids, porous media, underground diffusion of polluting substances; inverse problems for characteristic coefficients (conductivity, absorption) in various diffusion or hyperbolic equations, with applications to wave guides, taxis-diffusion in angiogenesis problems, etc. Regularization of solutions in collisional kinetic theory, in particular the non cutoff Boltzmann equations.

Standard Model, QFT and atomic physics: Rigorous analysis of Hamiltonians in particle physics: nonperturbative quantum electrodynamics , spectral theory for weak interactions and muonic atoms , derivation of van der Waals-London law; Quantum field theory in de Sitter space; scattering theory for nonrelativistic models on static space-times; Localization/delocalization properties for random Schrödinger operators ; bulk and edge states for magnetic Schrödinger operators.

Part of our activity gives rise to international collaborations with the following institutions: Aalborg University, Pontificia Universidad Catolica de Chile, Karlsruhe Institute of Technology, Kyoto Institute of Technology, Metz University, Moscow Institute of Physics and Technology.