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 |
Initial-boundary value problem for distributed order time-fractional diffusion equations
Asymptotic Analysis, 2019, 115 (1-2), pp.95-126. (10.3233/ASY-191532)
Multimode entanglement for fermions
26th Integrable Systems and Quantum Symmetries (ISQS26), Jul 2019, Prague, Czech Republic
A Dyson equation for non-equilibrium Green's functions in the partition-free setting
physica status solidi (b), 2019, 256 (7), pp.1800447. (10.1002/pssb.201800447)
Loi de van der Waals-London pour les systèmes d'atomes et de molécules relativistes
Physique mathématique [math-ph]. Université de Toulon, 2019. Français. (NNT : 2019TOUL0009)
Resolvent convergence to Dirac operators on planar domains
Annales Henri Poincaré, 2019, 20 (6), pp.1877-1891. (10.1007/s00023-019-00787-2)
Inverse moving source problems in electrodynamics
Inverse Problems, 2019, 35 (7), pp.075001. (10.1088/1361-6420/ab1496)
Application of the boundary control method to partial data Borg-Levinson inverse spectral problem
Mathematical Control and Related Fields, 2019, 9 (2), pp.289-312. (10.3934/mcrf.2019015)
Carleman estimate for the Schrödinger equation and application to magnetic inverse problems
Journal of Mathematical Analysis and Applications, 2019, 474 (1), pp.116-142. (10.1016/j.jmaa.2019.01.035)
Spectral analysis of sheared nanoribbons
Zeitschrift für Angewandte Mathematik und Physik = Journal of Applied mathematics and physics = Journal de mathématiques et de physique appliquées, 2019, 70 (2), pp.48. (10.1007/s00033-019-1090-6)
Hölder stably determining the time-dependent electromagnetic potential of the Schrödinger equation
SIAM Journal on Mathematical Analysis, 2019, 51 (2), pp.627-647. (10.1137/18M1197308)
