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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
Kenichi Fujishiro, Yavar Kian
Determination of Time Dependent Factors of Coefficients in Fractional Diffusion Equations
Mathematical Control and Related Fields, AIMS, 2016, 6 (2), pp.251-269. 〈10.3934/mcrf.2016003〉
Journal article
A. Ifa, N. M'Hadhbi, M. Rouleux
On Generalized Bohr–Sommerfeld Quantization Rules for Operators with PT Symmetry
Matematicheskie Zametki / Mathematical Notes, MAIK Nauka/Interperiodica, 2016, 99 (5), pp.676-684. 〈10.1134/S0001434616050060〉
Journal article
Vincent Bruneau, Nicolas Popoff
On the ground state energy of the Laplacian with a magnetic field created by a rectilinear current
Journal of Functional Analysis, Elsevier, 2015, 268 (5), 〈10.1016/j.jfa.2014.11.015〉
Journal article
Mourad Choulli, Laurent Kayser, Yavar Kian, Eric Soccorsi
Heat trace asymptotics and boundedness in the second order Sobolev space of isospectral potentials for the Dirichlet Laplacian
Asymptotic Analysis, IOS Press, 2015, 92 (3-4), pp.259-278. 〈10.3233/ASY-141277〉
Journal article
Mourad Choulli, Yavar Kian, Eric Soccorsi
Double logarithmic stability estimate in the identification of a scalar potential by a partial elliptic Dirichlet-to-Neumann map
Bulletin of the South Ural State University, South Ural State University, 2015, Mathematical Models and Computer Sciences, 8 (3), pp.78-94. 〈10.14529/mmp150305〉
Journal article
Patricia Gaitan, Hiroshi Isozaki, Olivier Poisson, Samuli Siltanen, Janne Tamminen
Inverse Problems for Time-Dependent Singular Heat Conductivities: Multi-Dimensional Case
Communications in Partial Differential Equations, Taylor & Francis, 2015, 40 (5), pp.837-877. 〈10.1080/03605302.2014.992533〉
Journal article
Otared Kavian, Yavar Kian, Eric Soccorsi
Uniqueness and stability results for an inverse spectral problem in a periodic waveguide
Journal de Mathématiques Pures et Appliquées, Elsevier, 2015, 104 (6), pp.1160-1189. 〈10.1016/j.matpur.2015.09.002〉
Journal article
Vojkan Jaksic, Jane Panangaden, Annalisa Panati, Claude-Alain Pillet
Energy conservation, counting statistics, and return to equilibrium
Letters in Mathematical Physics, Springer Verlag, 2015, 105 (7), pp.917-938. 〈10.1007/s11005-015-0769-7〉
Journal article
Philippe Briet, Hiba Hammedi, David Krejcirik
Hardy inequalities in globally twisted waveguides
Letters in Mathematical Physics, Springer Verlag, 2015, 105 (7), pp.939-958. 〈10.1007/s11005-015-0768-8〉
Journal article
Mourad Choulli, Eric Soccorsi
An inverse anisotropic conductivity problem induced by twisting a homogeneous cylindrical domain
Journal of Spectral Theory, European Mathematical Society, 2015, 5 (2), pp.295-329. 〈10.4171/JST/99〉
105 results

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