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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
Zalczer Sylvain PhD candidate
Email

List of Publications

101 results
Journal article
Yavar Kian
A multidimensional Borg-Levinson theorem for magnetic Schrödinger operators with partial spectral data
Journal of Spectral Theory, European Mathematical Society, 2018, 8, pp. 235-269
Journal article
Yavar Kian, Lauri Oksanen, Eric Soccorsi, Masahiro Yamamoto
Global uniqueness in an inverse problem for time fractional diffusion equations
Journal of Differential Equations, Elsevier, 2018, 264 (2), pp.1146-1170. 〈10.1016/j.jde.2017.09.032〉
Journal article
Guanghui Hu, Yavar Kian
Determination of singular time-dependent coefficients for wave equations from full and partial data
Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, 2018, 12 (3), pp.745-772
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, In press
Journal article
Jean-Marie Barbaroux, Horia Cornean, Edgardo Stockmeyer
Spectral gaps in Graphene antidot lattices
Integral Equations and Operator Theory, Springer Verlag, 2017, 89 (4), pp.631-646. 〈10.1007/s00020-017-2411-9〉
Journal article
Jean-Marie Barbaroux, Dirk Hundertmark, Tobias Ried, Semjon Vugalter
Strong smoothing for the non-cutoff homogeneous Boltzmann equation for Maxwellian molecules with Debye-Yukawa type interaction
Kinetic and Related Models , AIMS, 2017, 10 (4), pp.901-924. 〈10.3934/krm.2017036〉
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
2017
Preprint, Working paper
Yavar Kian
Recovery of non compactly supported coefficients of an elliptic equation on an infinite waveguide
2017
101 results

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