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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

ACHACHE Mahdi Postdoctoral researcher
Email
AMORIM Lucas PhD candidate
Email
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
KERRAOUI Nour 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
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
+33.4.91.26.95.36 Email
SOUSSI Yosra PhD candidate
Email
Zalczer Sylvain PhD candidate
Email

List of Publications

122 results
Preprint, Working paper
Jean-Marie Barbaroux, H Cornean, S Zalczer
Gap opening in the spectrum of some Dirac-like pseudo-differential operators
2020
Journal article
Guanghui Hu, Yavar Kian
Uniqueness and stability for the recovery of a time-dependent source and initial conditions in elastodynamics
Inverse Problems and Imaging , AIMS American Institute of Mathematical Sciences, In press
Journal article
Tristan Benoist, Annalisa Panati, Yan Pautrat
Heat Conservation and Fluctuations Between Quantum Reservoirs in the Two-Time Measurement Picture
Journal of Statistical Physics, Springer Verlag, In press, ⟨10.1007/s10955-019-02468-0⟩
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
Yavar Kian
Determination of non-compactly supported electromagnetic potentials in unbounded closed waveguide
Revista Matemática Iberoamericana, European Mathematical Society, In press, ⟨10.4171/rmi/1143⟩
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, In press
Journal article
Ali Feizmohammadi, Yavar Kian
Recovery of non-smooth coefficients appearing in anisotropic wave equations
SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2019, 51 (6), pp.4953-4976. ⟨10.1137/19M1251394⟩
Preprint, Working paper
Yavar Kian, Eric Soccorsi, Q Xue, Masahiro Yamamoto
Identification of time-varying source term in time-fractional diffusion equations
2019
Journal article
Philippe Briet, André Martinez
Molecular dynamics at an energy-level crossing
Journal of Differential Equations, Elsevier, 2019, 267 (10), pp.5662-5700. ⟨10.1016/j.jde.2019.06.004⟩
Journal article
Yavar Kian, Masahiro Yamamoto
Reconstruction and stable recovery of source terms appearing in diffusion equations
Inverse Problems, IOP Publishing, 2019, 35 (11), pp.115006. ⟨10.1088/1361-6420/ab2d42⟩
122 results

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