Centre de Physique Théorique

Home > Research teams > Quantum Dynamics and Spectral Analysis

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
Email
Barbaroux Jean-Marie University faculty
Chef de l’équipe « Dynamique quantique et analyse spectrale »
+33.4.91.26.95.03 Email
BRAHIM Philippe PhD candidate
+33.4.91.26.97.81 Email
Briet Philippe University faculty
Référent site UTLN
+33.4.91.26.95.11 Email
Gaïtan Patricia University faculty
+33.4.91.26.95.26 Email
KERRAOUI Nour PhD candidate
+33.4.91.26.97.90 Email
Kian Yavar University faculty
+33.4.91.26.95.29 Email
METIDJI Abdelmalek PhD candidate
Email
Panati Annalisa University faculty
+33.4.91.26.95.46 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
+33.4.91.26.95.37 Email

List of Publications

167 results
Preprint, Working paper
Ilya Bogaevsky, Michel Rouleux
Semi-classical Lagrangian intersections
2022
Preprint, Working paper
Jean-François Bougron, Alain Joye, Claude-Alain Pillet
Markovian Repeated Interaction Quantum Systems
2022
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
Journal article
Philippe Briet, David Krejcirik
Spectral optimisation of Dirac rectangles
Journal of Mathematical Physics, American Institute of Physics (AIP), 2022, 63, pp.013502. ⟨10.1063/5.0056278⟩
Preprint, Working paper
Yavar Kian, Éric Soccorsi, Faouzi Triki
Logarithmic stable recovery of the source and the initial state of time fractional diffusion equations
2021
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
Yavar Kian, Yosra Soussi
Stable recovery of noncompactly supported electromagnetic potentials in unbounded domain
Mathematical Methods in the Applied Sciences, Wiley, 2021, 44 (17), pp.13421-13447. ⟨10.1002/mma.7636⟩
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⟩
Thesis
Hamza Abdou Soimadou
Study of a mathematical model of nanoribbons
Théorie spectrale [math.SP]. Université de Toulon, 2021. Français
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⟩
167 results

Calendar