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 |
Markovian Repeated Interaction Quantum Systems
Reviews in Mathematical Physics, 2022, 34 (9), pp.2250028. (10.1142/S0129055X22500283)
Analysing the scattering of electromagnetic ultra wide band pulses from large scale objects by the use of wavelets
2022
Simultaneous determination of coefficients, internal sources and an obstacle of a diffusion equation from a single measurement
Inverse Problems, 2022, 38 (7), pp.075008. (10.1088/1361-6420/ac70f1)
Non autonomous maximal regularity for the fractional evolution equations
Journal of Evolution Equations, 2022, 22 (2), pp.48. (10.1007/s00028-022-00808-4)
Recovery of the Order of Derivation for Fractional Diffusion Equations in an Unknown Medium
SIAM Journal on Applied Mathematics, 2022, 82 (3), pp.1045-1067. (10.1137/21M1398264)
Semi-classical Lagrangian intersections
2022
Spectral properties of relativistic quantum waveguides
Annales Henri Poincaré, 2022, 23 (11), pp.4069-4114. (10.1007/s00023-022-01179-9)
A model of sheared nanoribbons
Nanosystems: Physics, Chemistry, Mathematics, 2022, 13 (1), pp.12-16. (10.17586/2220-8054-2022-13-1-12-16)
Identification of time-varying source term in time-fractional diffusion equations
Communications in Mathematical Sciences, 2022, 20 (1), pp.53 - 84. (10.4310/CMS.2022.v20.n1.a2)
Spectral optimisation of Dirac rectangles
Journal of Mathematical Physics, 2022, 63 (1), pp.013502. (10.1063/5.0056278)
