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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

AMORIM Lucas PhD candidate
Email
Barbaroux Jean-Marie University faculty
Chef de l’équipe « Dynamique quantique et analyse spectrale »
+33.4.91.26.95.03 Email
BRAHIM Philippe PhD candidate
+33.4.91.26.97.81 Email
Briet Philippe University faculty
Référent site UTLN
+33.4.91.26.95.11 Email
Gaïtan Patricia University faculty
+33.4.91.26.95.26 Email
KERRAOUI Nour PhD candidate
Email
Kian Yavar University faculty
+33.4.91.26.95.29 Email
Panati Annalisa University faculty
+33.4.91.26.95.46 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
+33.4.91.26.95.37 Email

List of Publications

143 results
Journal article
Cătălin Cârstea, Ali Feizmohammadi, Yavar Kian, Katya Krupchyk, Gunther Uhlmann
The Calderón inverse problem for isotropic quasilinear conductivities
Advances in Mathematics, Elsevier, 2021, 391, pp.107956. ⟨10.1016/j.aim.2021.107956⟩
Journal article
Bangti Jin, Yavar Kian
Recovering multiple fractional orders in time-fractional diffusion in an unknown medium
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2021, 477 (2253), pp.20210468. ⟨10.1098/rspa.2021.0468⟩
Journal article
Oleg Imanuvilov, Yavar Kian, Masahiro Yamamoto
Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate
Journal of Inverse and Ill-posed Problems, De Gruyter, In press, ⟨10.1515/jiip-2020-0089⟩
Conference paper
A Ifa, H Louati, Michel Rouleux
On semi-classical spectral series for an atom in a periodic polarized electric field
Days of Diffraction 2021, May 2021, Saint Petersbourg, Russia
Preprint, Working paper
Jean-Marie Barbaroux, Loïc Le Treust, Nicolas Raymond, Edgardo Stockmeyer
On the Dirac bag model in strong magnetic fields
2021
Journal article
Yavar Kian, Masahiro Yamamoto
Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations
Fractional Calculus and Applied Analysis, De Gruyter, 2021, 24 (1), pp.168-201. ⟨10.1515/fca-2021-0008⟩
Preprint, Working paper
William Borrelli, Philippe Briet, David Krejcirik, Thomas Ourmières-Bonafos
Spectral properties of relativistic quantum waveguides
2021
Preprint, Working paper
A. Yu. Anikin, S Dobrokhotov, Vladimir Nazaikinskii, Michel Rouleux
Semiclassical Green functions and Lagrangian intersection. Applications to the propagation of Bessel beams in non-homogeneous media
2021
Journal article
Jean-Marie Barbaroux, Loïc Le Treust, Nicolas Raymond, Edgardo Stockmeyer
On the semiclassical spectrum of the Dirichlet-Pauli operator
Journal of the European Mathematical Society, European Mathematical Society, In press
Journal article
Ali Feizmohammadi, Joonas Ilmavirta, Yavar Kian, Lauri Oksanen
Recovery of time dependent coefficients from boundary data for hyperbolic equations
Journal of Spectral Theory, European Mathematical Society, 2021, 11, pp.1107-1143
143 results

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