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 |
Inverse Problems for Time-Dependent Singular Heat Conductivities---One-Dimensional Case
SIAM Journal on Applied Mathematics, 2013, 45 (3), pp.1675-1690. (10.1137/120886510)
Approximation of the Integrals of the Gaussian Distribution of Asperity Heights in the Greenwood-Tripp Contact Model of Two Rough Surfaces Revisited
Journal of Applied Mathematics, 2013, 2013, 459280 (7 p.). (10.1155/2013/459280)
Stability result for a time dependent potential in a waveguide
Inverse Problems, 2013, 29
Inverse problem for a coupled parabolic system with discontinuous conductivities: One-dimensional case
Inverse Problems and Imaging , 2013, (10.3934/ipi.2013.7.159)
Exponential decay and resonances in a driven system
Journal of Mathematical Analysis and Applications, 2012, 396 (02), pp.513-522. (10.1016/j.jmaa.2012.06.040)
A rigorous approach to the magnetic response in disordered systems
Reviews in Mathematical Physics, 2012, 24 (08), pp.1250022. (10.1142/S0129055X12500225)
Identification of the twisting function for the dynamic Schrödinger operator in a quantum waveguide
2012
The semiclassical Maupertuis-Jacobi correspondence for quasi-periodic Hamiltonian flows: stable and unstable spectra
Days on Diffraction 2012, May 2012, St. Petersburg Russia. pp.59-64, (10.1109/DD.2012.6402752)
MIMO capacity for deterministic channel models: sublinear growth
Mathematical Methods in the Applied Sciences, 2012, 36 (1), pp.18-27. (10.1002/mma.2565)
A rigorous proof of the Landau-Peierls formula and much more
Annales Henri Poincaré, 2012, 13 (1), pp.1-40. (10.1007/s00023-011-0128-x)
