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 |
Removal of UV cutoff for the Nelson model with variable coefficients
Letters in Mathematical Physics, 2012, 101 (3), pp.305-322. (10.1007/s11005-012-0577-2)
On the guided states of 3D biperiodic Schrödinger operators
Communications in Partial Differential Equations, 2012, 37 (10), pp.1805-1838
On the ground state energy of the translation invariant Pauli-Fierz Model. II.
Documenta Mathematica, 2012, 17, pp.401-415
Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle
Cubo, a Mathematical Journal, 2012, 14 (2), pp.153-173. (10.4067/S0719-06462012000200008)
Absence of ground state for the Nelson model on static space-times
Journal of Functional Analysis, 2012, 262 (01), pp.273-299. (10.1016/j.jfa.2011.09.010)
Inverse boundary value problem for the dynamical heterogeneous Maxwell system
Inverse Problems, 2012, 28 (9), pp.095009. (10.1088/0266-5611/28/9/095009)
Adiabatic non-equilibrium steady states in the partition free approach
Annales Henri Poincaré, 2012, 13 (4), pp.827-856. (10.1007/s00023-011-0144-x)
Probing for inclusions in heat conductive bodies
Inverse Problems and Imaging , 2012, 6 (3), pp.423 - 446. (10.3934/ipi.2012.6.423)
Infrared problem for the Nelson model on static space-times
Communications in Mathematical Physics, 2011, 308 (2), pp.543-566. (10.1007/s00220-011-1289-7)
Formules de courant dans les systèmes mésoscopiques
Mathématiques générales [math.GM]. Université de Toulon, 2011. Français. (NNT : 2011TOUL0011)
