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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 »
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Boughanja Yosra PhD candidate
Briet Philippe University faculty
Référent site UTLN
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Gaïtan Patricia University faculty
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Hamza Abdou-Soimadou PhD candidate
Hartig Michael PhD candidate
Kian Yavar University faculty
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Leopold Elie University faculty
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M’Madi-Issimail Mohamed-Mouneime PhD candidate
Panati Annalisa University faculty
Pillet Claude-Alain University faculty
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Rouleux Michel University faculty
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Soccorsi Eric University faculty
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SOUSSI Yosra PhD candidate
Zalczer Sylvain PhD candidate

List of Publications

118 results
Accreditation to supervise research
Yavar Kian
Etude de problèmes inverses et directs pour différentes équations aux dérivées partielles
Analysis of PDEs [math.AP]. Université d'Aix-Marseille, 2017
Journal article
Mourad Choulli, Yavar Kian, Eric Soccorsi
On the Calderón problem in periodic cylindrical domain with partial Dirichlet and Neumann data
Mathematical Methods in the Applied Sciences, Wiley, 2017, 40 (16), pp.5959-5974. ⟨10.1002/mma.4446⟩
Preprint, Working paper
Zhiyuan Li, Yavar Kian, Eric Soccorsi
Initial-boundary value problem for distributed order time-fractional diffusion equations
Journal article
Jean-Marie Barbaroux, Dirk Hundertmark, Tobias Ried, Semjon Vugalter
Gevrey Smoothing for Weak Solutions of the Fully Nonlinear Homogeneous Boltzmann and Kac Equations Without Cutoff for Maxwellian Molecules
Archives of rational mechanics and analysis, Springer-Verlag, 2017, 225 (2), pp. 601-661. ⟨10.1007/s00205-017-1101-8⟩
Journal article
A. Yu. Anikin, S. Yu. Dobrokhotov, V. E. Nazaikinskii, M. Rouleux
Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides
Доклады Академии Наук / Doklady Mathematics, MAIK Nauka/Interperiodica, 2017, 96 (1), pp.406 - 410. ⟨10.1134/S1064562417040275⟩
Conference paper
Anatoly Anikin, Serguei Dobrokhotov, Vladimir Nazaikinskii, Michel Rouleux
Asymptotics of Green function for the linear waves equations in a domain with a non-uniform bottom
Days on Diffraction 2017, Jun 2017, St. Petersbourg, Russia. pp.18-23, ⟨10.1109/DD.2017.8167988⟩
Conference paper
Michel Rouleux
Generalized Pareto optimum and semi-classical spinors
25th International Conference on Integrable Systems and Quantum Symmetries (ISQS), Jun 2017, Prague, Czech Republic. pp.012034, ⟨10.1088/1742-6596/965/1/012034⟩
Journal article
Philippe Briet, André Martinez
Estimates On The Molecular Dynamics For The Predissociation Process
Journal of Spectral Theory, European Mathematical Society, 2017, 7 (2), pp.487-517. ⟨10.4171/JST/170⟩
Journal article
Patricia Gaitan, Hadjer Ouzzane
Stability result for two coefficients in a coupled hyperbolic-parabolic system
Journal of Inverse and Ill-posed Problems, De Gruyter, 2017, 25 (3), ⟨10.1515/jiip-2015-0017⟩
Journal article
Benjamin Landon, Jane Panangaden, Annalisa Panati, Justine Zwicker
Reflection probabilities of one-dimensional Schrödinger operators and scattering theory
Annales Henri Poincaré, Springer Verlag, 2017, 18 (6), pp.2075-2085. ⟨10.1007/s00023-016-0543-0⟩
118 results