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Quantum Dynamics and Spectral Analysis

Group “Classical and Quantum Dynamical Systems”

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.

Directory of Members

Barbaroux Jean-Marie University faculty
Chef de l’équipe « Dynamique quantique et analyse spectrale »
+33.4.91.26.95.17 Email
Boughanja Yosra PhD candidate
Email
Briet Philippe University faculty
Référent site UTLN
+33.4.91.26.95.11 Email
Cristofol Michel Guest
+33.4.91.55.14.00 Email
Gaïtan Patricia University faculty
+33.4.91.26.95.29 Email
Hamza Abdou-Soimadou PhD candidate
Email
Hartig Michael PhD candidate
Email
Kian Yavar University faculty
+33.4.91.26.95.29 Email
Le Treust Loïc Guest
Email
Leopold Elie University faculty
+33.4.91.26.95.10 Email
M’Madi-Issimail Mohamed-Mouneime PhD candidate
Email
Panati Annalisa University faculty
Email
Pillet Claude-Alain University faculty
+33.4.91.26.95.32 Email
Rouleux Michel University faculty
+33.4.91.26.97.97 Email
Soccorsi Eric University faculty
+33.4.91.26.95.36 Email
SOUSSI Yosra PhD candidate
Email
Zalczer Sylvain PhD candidate
Email

List of Publications

117 results
Preprint, Working paper
Guanghui Hu, Yavar Kian
Uniqueness and stability for the recovery of a time-dependent source and initial conditions in elastodynamics
2018
Preprint, Working paper
Jean-Marie Barbaroux, Loïc Le Treust, Nicolas Raymond, Edgardo Stockmeyer
On the semiclassical spectrum of the Dirichlet-Pauli operator
2018
Preprint, Working paper
Mourad Bellassoued, Mourad Choulli, David Dos Santos Ferreira, Yavar Kian, Plamen Stefanov
A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold
2018
Conference paper
Abdelwaheb Ifa, Michel Rouleux
Hamiltonien de Bogoliubov-de Gennes en 1-D avec symétrie PT: règles de quantification généralisées de Bohr-Sommerfeld.
Group 32 (32nd International Colloquium on Group Theoretical Methods in Physics), Jul 2018, Prague, Czech Republic
Preprint, Working paper
Yavar Kian
On the determination of nonlinear terms appearing in semilinear hyperbolic equations
2018
Conference paper
A Anikin, S. Dobrokhotov, V Nazaikinskii, Michel Rouleux
Semi-classical Green functions
International Conference on Days on Diffraction (DD), Jun 2018, Saint Petersbourg, Russia. pp.17-23, ⟨10.1109/DD.2018.8553179⟩
Preprint, Working paper
Yavar Kian, Yaroslav Kurylev, Matti Lassas, Lauri Oksanen
Hyperbolic inverse problem with data on disjoint sets
2018
Journal article
M Bellassoued, Y Kian, Eric Soccorsi
An inverse problem for the magnetic Schrödinger equation in infinite cylindrical domains
Publications of the Research Institute for Mathematical Sciences, European Mathematical Society, 2018, 54 (4), pp.679-728. ⟨10.4171/PRIMS/54-4-1⟩
Journal article
Gang Bao, Guanghui Hu, Yavar Kian, Tao Yin
Inverse source problems in elastodynamics
Inverse Problems, IOP Publishing, 2018, 34, 4, pp.045009
Journal article
Abdelwaheb Ifa, Hanen Louati, Michel Rouleux
Bohr-Sommerfeld Quantization Rules Revisited: The Method of Positive Commutators
Journal of mathematical sciences, the university of Tokyo, In press, J. Math. Sci. Univ. Tokyo, 25, p.91-137
117 results

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