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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
Abdelwaheb Ifa, Hanen Louati, Michel Rouleux
Bohr-Sommerfeld Quantization Rules Revisited: The Method of Positive Commutators
Journal of mathematical sciences, the university of Tokyo, In press
Journal article
Yavar Kian, Eric Soccorsi, Masahiro Yamamoto
On Time-Fractional Diffusion Equations with Space-Dependent Variable Order
Annales Henri Poincaré, Springer Verlag, In press, 〈10.1007/s00023-018-0734-y〉
Journal article
Mourad Choulli, Yavar Kian
Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term
Journal de Mathématiques Pures et Appliquées, Elsevier, 2018, 114, pp.235-261. 〈10.1016/j.matpur.2017.12.003〉
Journal article
Gang Bao, Guanghui Hu, Yavar Kian, Tao Yin
Inverse source problems in elastodynamics
Inverse Problems, IOP Publishing, 2018, 34, 4, pp.045009
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
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, 2018, 54, pp.679-728
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
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
Mourad Choulli, Yavar Kian, Eric Soccorsi
Stability result for elliptic inverse periodic coefficient problem by partial Dirichlet-to-Neumann map
Journal of Spectral Theory, European Mathematical Society, 2018, 8 (2), pp.733-768. 〈10.4171/JST/212〉
Journal article
Yavar Kian
Recovery of non compactly supported coefficients of an elliptic equation on an infinite waveguide
Journal of the Institute of Mathematics of Jussieu, Cambridge University Press (CUP), In press
105 results

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