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 |
Strong smoothing for the non-cutoff homogeneous Boltzmann equation for Maxwellian molecules with Debye-Yukawa type interaction
Kinetic and Related Models , 2017, 10 (4), pp.901-924. (10.3934/krm.2017036)
Spectral gaps in Graphene antidot lattices
Integral Equations and Operator Theory, 2017, 89 (4), pp.631-646. (10.1007/s00020-017-2411-9)
Study of inverse and direct problems for different partial differential equations
Analysis of PDEs [math.AP]. Université d'Aix-Marseille, 2017
On the Calderón problem in periodic cylindrical domain with partial Dirichlet and Neumann data
Mathematical Methods in the Applied Sciences, 2017, 40 (16), pp.5959-5974. (10.1002/mma.4446)
On the Nature of Energy Full Statistics: fluctuations’ control and heavy-tailed distributions and ultraviolet regularisation
Mathematical Questions and Challenges in Quantum Electrodynamics and its Applications, Sep 2017, Oberwolfach, Germany. pp.2539-2599, (10.4171/OWR/2017/41)
Gevrey Smoothing for Weak Solutions of the Fully Nonlinear Homogeneous Boltzmann and Kac Equations Without Cutoff for Maxwellian Molecules
Archive for Rational Mechanics and Analysis, 2017, 225 (2), pp. 601-661. (10.1007/s00205-017-1101-8)
Maslov canonical operator on a pair of Lagrangian manifolds and asymptotic solutions of stationary equations with localized right-hand sides
Доклады Академии Наук / Doklady Mathematics, 2017, 96 (1), pp.406 - 410. (10.1134/S1064562417040275)
Asymptotics of Green function for the linear waves equations in a domain with a non-uniform bottom
Days on Diffraction 2017, Jun 2017, St. Petersbourg, Russia. pp.18-23, (10.1109/DD.2017.8167988)
Generalized Pareto optimum and semi-classical spinors
25th International Conference on Integrable Systems and Quantum Symmetries (ISQS), Jun 2017, Prague, Czech Republic. pp.012034, (10.1088/1742-6596/965/1/012034)
Reflection probabilities of one-dimensional Schrödinger operators and scattering theory
Annales Henri Poincaré, 2017, 18 (6), pp.2075-2085. (10.1007/s00023-016-0543-0)
