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 |
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
Full statistics of energy conservation in two times measurement protocols
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics [2001-2015], 2015, 92 (3), pp.032115. (10.1103/PhysRevE.92.032115)
Energy conservation, counting statistics, and return to equilibrium
Letters in Mathematical Physics, 2015, 105 (7), pp.917-938. (10.1007/s11005-015-0769-7)
Uniqueness and stability results for an inverse spectral problem in a periodic waveguide
Journal de Mathématiques Pures et Appliquées, 2015, 104 (6), pp.1160-1189. (10.1016/j.matpur.2015.09.002)
Double logarithmic stability estimate in the identification of a scalar potential by a partial elliptic Dirichlet-to-Neumann map
Bulletin of the South Ural State University, 2015, Mathematical Models and Computer Sciences, 8 (3), pp.78-94. (10.14529/mmp150305)
Stable determination of time-dependent scalar potential from boundary measurements in a periodic quantum waveguide
SIAM Journal on Mathematical Analysis, 2015, 47 (6), pp.4536-4558. (10.1137/140986268)
Stark resonances in 2-dimensional curved quantum waveguides
Reports on Mathematical Physics, 2015, 76 (3), pp.317-338
Hölder stable determination of a quantum scalar potential in unbounded cylindrical domains
Journal of Mathematical Analysis and Applications, 2015, 426 (1), pp.194-210. (10.1016/j.jmaa.2015.01.028)
Hardy inequalities in globally twisted waveguides
Letters in Mathematical Physics, 2015, 105 (7), pp.939-958. (10.1007/s11005-015-0768-8)
