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 emeritus | +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 emeritus | +33.4.91.26.97.97 | Contact |
| SOCCORSI | Eric | Research teacher | +33.4.91.26.95.37 | Contact |
Some trace monotonicity properties and applications
Annals of Functional Analysis, 2016, 7 (3), pp.394-401. (10.1215/20088752-3605258)
Regular Bohr-Sommerfeld quantization rules for a h-pseudo-differential operator. The method of positive commutators
International Conference of the Euro-Maghreb Laboratory of Mathematics and their Interactions LEM2I-2016., Apr 2016, Hammamet, Tunisia. pp.2593, (10.46298/arima.2593)
Determination of Time Dependent Factors of Coefficients in Fractional Diffusion Equations
Mathematical Control and Related Fields, 2016, 6 (2), pp.251-269. (10.3934/mcrf.2016003)
Crystalline conductance and absolutely continuous spectrum of 1D samples
Letters in Mathematical Physics, 2016, 106 (6), pp.787-797. (10.1007/s11005-016-0844-8)
Limiting absorption principle for the Magnetic Dirichlet Laplacian in a half-plane.
Communications in Partial Differential Equations, 2016, 41 (6), pp.879-893. (10.1080/03605302.2016.1167081)
On Generalized Bohr–Sommerfeld Quantization Rules for Operators with PT Symmetry
Matematicheskie Zametki / Mathematical Notes, 2016, 99 (5), pp.676-684. (10.1134/S0001434616050060)
Stability in the determination of a time-dependent coefficient for wave equations from partial data
Journal of Mathematical Analysis and Applications, 2016, 436 (1), pp.408-428. (10.1016/j.jmaa.2015.12.018)
Localization error estimate for the massless relativistic kinetic energy operator
Mathematical Modelling of Natural Phenomena, 2016, 11 (2), pp.36-43. (10.1051/mmnp/201611203)
Dynamical localization of Dirac particles in electromagnetic fields with dominating magnetic potentials
Journal of Differential Equations, 2016, 260 (7), pp.5912-5925. (10.1016/j.jde.2015.12.021)
Recovery of time-dependent damping coefficients and potentials appearing in wave equations from partial data
SIAM Journal on Mathematical Analysis, 2016, 48 (6), pp.4021-4046
