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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

105 results
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
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〉
Preprint, Working paper
Yavar Kian, Eric Soccorsi
Hölder stably determining the time-dependent electromagnetic potential of the Schrödinger equation
2017
Book Section
Philippe Briet, Hiba Hammedi
Twisted waveguide with a Neumann window
Functional Analysis and Operator Theory for Quantum Physics : The Pavel Exner Anniversary Volume, European Mathematical Society, pp.161-175, 2017, EMS Series of Congress Reports, 978-3-03719-175-0. 〈10.4171/175-1/8〉
Preprint, Working paper
Y Kian, M Morancey, L Oksanen
Application of the boundary control method to partial data Borg-Levinson inverse spectral problem
2017
Thesis
Hanen Louati
Semi-classical quantization rules for a periodic orbit of hyperbolic type
Mathématiques générales [math.GM]. Université de Toulon, 2017. Français. 〈NNT : 2017TOUL0004〉
Preprint, Working paper
Yavar Kian, Diomba Sambou, Eric Soccorsi
Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide
2017
Journal article
Yavar Kian, Masahiro Yamamoto
On Existence and Uniqueness of Solutions for Semilinear Fractional Wave Equations
Fractional Calculus and Applied Analysis, De Gruyter, 2017, 20 (1), pp.117-138. 〈10.1515/fca-2017-0006〉
Journal article
Yavar Kian, Lauri Oksanen
Recovery of time-dependent coefficient on Riemannian manifold for hyperbolic equations
International Mathematical Research Notices, Oxford University Press, 2017, pp.rnx263. 〈10.1093/imrn/rnx263〉
Journal article
Yavar Kian
Unique determination of a time-dependent potential for wave equations from partial data
Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2017, 34 (4), pp.973-990. 〈10.1016/j.anihpc.2016.07.003〉
105 results

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