Group “Classical and Quantum Dynamical Systems”
The main research focus of the Quantum Dynamics and Spectral Analysis team is the mathematical study of problems arising in physics and their applications. Most of our activity concerns the spectral and scattering properties of models of nanostructures, models in atomic physics and particle physics in quantum field theory, the properties of solutions of the PDEs of physics, and the properties of uniqueness, stability, and reconstruction in inverse problems.
The main strengths of our scientific activity:
Nanostructures: Propagation properties of waves in optical fibers and quantum waveguides; spectral properties of differential operators on graphs; study of the semiconducting character and gap opening in graphene samples with periodic perforations.
PDEs and inverse problems: Convergence-to-equilibrium properties for dilute particle gases and regularization of solutions to the nonlinear Kac and Boltzmann equations; inverse problems in models of anomalous diffusion involving fractional-time equations (complex fluids, porous media, diffusion of pollutants in soil); inverse problems for characteristic coefficients (diffusion, absorption, etc.), with applications to waveguides, angiogenesis, Black–Scholes models, etc.
Standard Model, QFT and atomic physics: Rigorous analysis of Hamiltonians in particle physics: non-perturbative quantum electrodynamics; spectral theory for weak interaction models and muonic atoms; derivation of the Van der Waals–London laws; spectral theory in quantum field theory on de Sitter spaces and scattering theory on Lorentzian manifolds in QED; edge currents and surface states for magnetic Schrödinger operators.
| ALVAREZ | Benjamin | Research teacher | +33.4.91.26.97.92 | Contact |
| BARBAROUX | Jean-Marie | Research teacher Team leader « Quantum Dynamics and Spectral Analysis » | +33.4.91.26.95.03 | Contact |
| BRIET | Philippe | Research teacher | +33.4.91.26.95.11 | Contact |
| GOUTTENEGRE | Hugo | Ph.D. | Contact | |
| PANATI | Annalisa | Research teacher | +33.4.91.26.95.46 | Contact |
| PILLET | Claude-Alain | Research teacher | +33.4.91.26.95.32 | Contact |
| ROULEUX | Michel | Research teacher | +33.4.91.26.97.97 | Contact |
| SOCCORSI | Eric | Research teacher | +33.4.91.26.95.37 | Contact |
Reconstruction of a Space-Time-Dependent Source in Subdiffusion Models via a Perturbation Approach
SIAM Journal on Mathematical Analysis, 2021, 53 (4), pp.4445-4473. (10.1137/21M1397295)
Gap opening in the spectrum of some Dirac-like pseudo-differential operators
Revue roumaine de mathématiques pures et appliquées, 2021, 66 (3-4), pp.597-616
Stable recovery of a non-compactly supported coefficient of a Schrödinger equation on an infinite waveguide
Inverse Problems and Imaging , 2021, 15 (5), pp.929-950. (10.3934/ipi.2021022)
Recovery of time dependent coefficients from boundary data for hyperbolic equations
Journal of Spectral Theory, 2021, 11 (3), pp.1107-1143. (10.4171/JST/367)
Inégalités de stabilité dans les problèmes inverses pour équations parabolique et de transport
Mathématiques [math]. Aix Marseille Université; Université de Tunis El Manar, 2020. Français. (NNT : )
Hölder Stable Recovery of Time-Dependent Electromagnetic Potentials Appearing in a Dynamical Anisotropic Schrödinger Equation
Inverse Problems and Imaging , 2020, 14 (5), pp.819-839. (10.3934/ipi.2020038)
Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide
Applicable Analysis, 2020, 99 (13), pp.2210-2228. (10.1080/00036811.2018.1557324)
Recovery of non compactly supported coefficients of an elliptic equation on an infinite waveguide
Journal of the Institute of Mathematics of Jussieu, 2020, 19 (5), pp.1573 - 1600. (10.1017/S1474748018000488)
Propriétés spectrales de modèles de graphène périodique et désordonné
Mathématiques générales [math.GM]. Université de Toulon, 2020. Français. (NNT : 2020TOUL0003)
Uniqueness and stability for the recovery of a time-dependent source in elastodynamics
Inverse Problems and Imaging , 2020, 14 (3), pp.463-487. (10.3934/ipi.2020022)
