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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
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
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

118 results
Journal article
Michel Cristofol, Shumin Li, Eric Soccorsi
Determining the waveguide conductivity in a hyperbolic equation from a single measurement on the lateral boundary
Mathematical Control and Related Fields, AIMS, 2016, 6 (3), pp.407 - 427. ⟨10.3934/mcrf.2016009⟩
Journal article
Philippe Briet, André Martinez
Dynamique moléculaire de la prédissociation
Comptes Rendus Mathématique, Elsevier Masson, 2016, 354 (9), pp.912-915. ⟨10.1016/j.crma.2016.06.003⟩
Conference paper
Hanen Louati, Michel Rouleux
Semi-classical quantization rules for a periodic orbit of hyperbolic type
Days on Diffraction (DD), 2016, Jun 2016, Saint-Petersbourg, Russia. pp.112-117, ⟨10.1109/DD.2016.7756858⟩
Journal article
Youssef Mejri
Stability estimate for the aligned magnetic field in a periodic quantum waveguide from Dirichlet-to-Neumann map
Journal of Mathematical Physics, American Institute of Physics (AIP), 2016, 57 (6), pp.061502 ⟨10.1063/1.4953687⟩
Journal article
J. -M. Combes, P. D. Hislop
Some trace monotonicity properties and applications
Annals of Functional Analysis, Mashhad : Tusi Mathematical Research Group, 2016, 7 (3), pp.394-401. ⟨10.1215/20088752-3605258⟩
Conference paper
Abdelwaheb Ifa, Michel Rouleux
Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator. The method of positive commutators
International Conference of the Euro-Maghreb Laboratory of Mathematics and their Interactions LEM2I-2016., Apr 2016, Hammamet, Tunisia. pp.2593
Journal article
A. Ifa, N. M'Hadhbi, M. Rouleux
On Generalized Bohr–Sommerfeld Quantization Rules for Operators with PT Symmetry
Matematicheskie Zametki / Mathematical Notes, MAIK Nauka/Interperiodica, 2016, 99 (5), pp.676-684. ⟨10.1134/S0001434616050060⟩
Journal article
Yavar Kian
Stability in the determination of a time-dependent coefficient for wave equations from partial data
Journal of Mathematical Analysis and Applications, Elsevier, 2016, 436 (1), pp.408-428. ⟨10.1016/j.jmaa.2015.12.018⟩
Journal article
Jean-Marie Barbaroux, Vitali Vougalter, Semjon Vugalter
Localization error estimate for the massless relativistic kinetic energy operator
Mathematical Modelling of Natural Phenomena, EDP Sciences, 2016, 11 (2), pp.36-43. ⟨10.1051/mmnp/201611203⟩
Journal article
Kenichi Fujishiro, Yavar Kian
Determination of Time Dependent Factors of Coefficients in Fractional Diffusion Equations
Mathematical Control and Related Fields, AIMS, 2016, 6 (2), pp.251-269. ⟨10.3934/mcrf.2016003⟩
118 results

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