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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
SOUSSI Yosra PhD candidate
Email
Zalczer Sylvain PhD candidate
Email

List of Publications

110 results
Preprint, Working paper
Vojkan Jaksic, Vahagn Nersesyan, Claude-Alain Pillet, Armen Shirikyan
Large deviations and entropy production in viscous fluid flows
2019
Journal article
Tristan Benoist, Annalisa Panati, Renaud Raquépas
Control of fluctuations and heavy tails for heat variation in the two-time measurement framework
Annales Henri Poincaré, Springer Verlag, 2019, 20 (2), pp.631-674. 〈10.1007/s00023-018-0743-x〉
Preprint, Working paper
Pedro Caro, Yavar Kian
Determination of convection terms and quasi-linearities appearing in diffusion equations
2019
Preprint, Working paper
Yavar Kian
Determination of non-compactly supported electromagnetic potentials in unbounded closed waveguide
2019
Journal article
Yavar Kian, Eric Soccorsi
Hölder stably determining the time-dependent electromagnetic potential of the Schrödinger equation
SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, In press
Journal article
Yavar Kian, Diomba Sambou, Eric Soccorsi
Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide
Applicable Analysis, Taylor & Francis, In press
Preprint, Working paper
Philippe Briet, André Martinez
Molecular dynamics at an energy-level crossing
2018
Preprint, Working paper
Guanghui Hu, Yavar Kian, Peijun Li, Yue Zhao
INVERSE MOVING SOURCE PROBLEMS IN ELECTRODYNAMICS
2018
Preprint, Working paper
Tristan Benoist, Annalisa Panati, Yan Pautrat
Heat conservation and fluctuations for open quantum systems in the Two-Time Measurement picture
2018
Preprint, Working paper
Guanghui Hu, Yavar Kian
Uniqueness and stability for the recovery of a time-dependent source and initial conditions in elastodynamics
2018
110 results

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