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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

AMORIM Lucas PhD candidate
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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KERRAOUI Nour PhD candidate
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Kian Yavar University faculty
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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

154 results
Journal article
Yavar Kian, Eric Soccorsi, Q Xue, Masahiro Yamamoto
Identification of time-varying source term in time-fractional diffusion equations
Communications in Mathematical Sciences, International Press, 2022, 20, pp.53 - 84
Preprint, Working paper
Yavar Kian, Éric Soccorsi, Faouzi Triki
Logarithmic stable recovery of the source and the initial state of time fractional diffusion equations
Preprint, Working paper
Philippe Briet, David Krejcirik
Spectral optimisation of Dirac rectangles
Journal article
Cătălin Cârstea, Ali Feizmohammadi, Yavar Kian, Katya Krupchyk, Gunther Uhlmann
The Calderón inverse problem for isotropic quasilinear conductivities
Advances in Mathematics, Elsevier, 2021, 391, pp.107956. ⟨10.1016/j.aim.2021.107956⟩
Journal article
Bangti Jin, Yavar Kian
Recovering multiple fractional orders in time-fractional diffusion in an unknown medium
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2021, 477 (2253), pp.20210468. ⟨10.1098/rspa.2021.0468⟩
Journal article
Oleg Imanuvilov, Yavar Kian, Masahiro Yamamoto
Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate
Journal of Inverse and Ill-posed Problems, De Gruyter, In press, ⟨10.1515/jiip-2020-0089⟩
Journal article
Philippe Briet, J.-C Cuenin, L Golinskii, Stanislas Kupin
Lieb–Thirring inequalities for an effective Hamiltonian of bilayer graphene
Journal of Spectral Theory, European Mathematical Society, 2021, 11 (3), pp.1145-1178. ⟨10.4171/jst/368⟩
Journal article
Vojkan Jaksic, Vahagn Nersesyan, Claude-Alain Pillet, Armen Shirikyan
Large deviations and entropy production in viscous fluid flows
Archive for Rational Mechanics and Analysis, Springer Verlag, 2021, 240, pp.1675-1725. ⟨10.1007/s00205-021-01646-3⟩
Conference paper
A Ifa, H Louati, Michel Rouleux
On semi-classical spectral series for an atom in a periodic polarized electric field
Days of Diffraction 2021, May 2021, Saint Petersbourg, Russia
Preprint, Working paper
Jean-Marie Barbaroux, Loïc Le Treust, Nicolas Raymond, Edgardo Stockmeyer
On the Dirac bag model in strong magnetic fields
154 results


January 2022 :

Nothing for this month

December 2021 | February 2022