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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

ALVAREZ Benjamin University faculty
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Barbaroux Jean-Marie University faculty
Chef de l’équipe « Dynamique quantique et analyse spectrale »
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BRAHIM Philippe PhD candidate
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Briet Philippe University faculty
Référent site UTLN
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Gaïtan Patricia University faculty
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Kian Yavar University faculty
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METIDJI Abdelmalek PhD candidate
Panati Annalisa University faculty
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Pillet Claude-Alain University faculty
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Rouleux Michel University faculty
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Soccorsi Eric University faculty
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List of Publications

168 results
Journal article
Yavar Kian, Eric Soccorsi, Masahiro Yamamoto
On Time-Fractional Diffusion Equations with Space-Dependent Variable Order
Annales Henri Poincaré, Springer Verlag, 2018, 19 (12), pp.3855-3881. ⟨10.1007/s00023-018-0734-y⟩
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 (4), pp.679-728. ⟨10.4171/PRIMS/54-4-1⟩
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. ⟨10.3934/ipi.2018032⟩
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 (1), pp.235-269. ⟨10.4171/JST/195⟩
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
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
Jean-Marie Barbaroux, Dirk Hundertmark, Tobias Ried, Semjon Vugalter
Strong smoothing for the non-cutoff homogeneous Boltzmann equation for Maxwellian molecules with Debye-Yukawa type interaction
Kinetic and Related Models , AIMS, 2017, 10 (4), pp.901-924. ⟨10.3934/krm.2017036⟩
Journal article
Jean-Marie Barbaroux, Horia D. Cornean, Edgardo Stockmeyer
Spectral gaps in Graphene antidot lattices
Integral Equations and Operator Theory, Springer Verlag, 2017, 89 (4), pp.631-646. ⟨10.1007/s00020-017-2411-9⟩
Accreditation to supervise research
Yavar Kian
Etude de problèmes inverses et directs pour différentes équations aux dérivées partielles
Analysis of PDEs [math.AP]. Université d'Aix-Marseille, 2017
Journal article
Mourad Choulli, Yavar Kian, Eric Soccorsi
On the Calderón problem in periodic cylindrical domain with partial Dirichlet and Neumann data
Mathematical Methods in the Applied Sciences, Wiley, 2017, 40 (16), pp.5959-5974. ⟨10.1002/mma.4446⟩
168 results