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 |
Control of fluctuations and heavy tails for heat variation in the two-time measurement framework
Annales Henri Poincaré, 2019, 20 (2), pp.631-674. (10.1007/s00023-018-0743-x)
Determination of convection terms and quasi-linearities appearing in diffusion equations
2019
Unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets
Journal of Differential Equations, 2019, 267 (4), pp.2210-2238. (10.1016/j.jde.2019.03.008)
Local decay for weak interactions with massless particles
Journal of Spectral Theory, 2019, 9 (2), pp.453-512. (10.4171/JST/253)
Recovery of time-dependent coefficient on Riemannian manifold for hyperbolic equations
International Mathematics Research Notices, 2019, 2019 (16), pp.5087-5126. (10.1093/imrn/rnx263)
Localization for Gapped Dirac Hamiltonians with Random Perturbations: Application to Graphene Antidot Lattices
Documenta Mathematica, 2019, 24, pp.65-93. (10.25537/dm.2019v24.65-93)
Semi-classical quantum maps of semi-hyperbolic type
International Conference on PDE's and Applications in Memory of Professor B.Yu.Sternin , Nov 2018, Moscou, Russia
A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold
2018
The one dimensional semi-classical Bogoliubov-de Gennes Hamiltonian with PT symmetry: generalized Bohr-Sommerfeld quantization rules.
Group 32 (32nd International Colloquium on Group Theoretical Methods in Physics), Jul 2018, Prague, Czech Republic. pp.012049, (10.1088/1742-6596/1194/1/012049)
Semi-classical Green functions
International Conference on Days on Diffraction (DD), Jun 2018, Saint Petersbourg, Russia. pp.17-23, (10.1109/DD.2018.8553179)
