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 |
Etude théorique du second point critique dans le gaz de Bose
Physique mathématique [math-ph]. Université de la Méditerranée - Aix-Marseille II, 2010. Français. (NNT : )
The second critical point for the Perfect Bose gas in quasi-one-dimensional traps
2010
A nonlinear ordinary differential equation associated with the quantum sojourn time
Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), pp.474007. (10.1088/1751-8113/43/47/474007)
Conductivity and the current-current correlation measure
Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), pp.474010. (10.1088/1751-8113/43/47/474010)
Quantitative estimates on the binding energy for Hydrogen in non-relativistic QED
Annales Henri Poincaré, 2010, 11 (8), pp.1487-1544. (10.1142/S0129055X14500160)
On the relation between measures defining the Stieltjes and the inverted Stieltjes functions
Ukrainian Mathematical Journal, 2010, 62 (3), pp.373-379. (10.1007/s11253-010-0360-4)
General algorithm of computation of c-table and detection of valleys
Ukrainian Mathematical Journal, 2010, 62 (6), pp.882-893. (10.1007/s11253-010-0397-4)
Asymptotic behaviours and general recurrence relations
Applied Numerical Mathematics: an IMACS journal, 2010, 60 (12), pp.1352-1363. (10.1016/j.apnum.2010.08.001)
Simultaneous Identification of the Diffusion Coefficient and the Potential for the Schrôdinger Operator with one Observation
Inverse Problems, 2010, 26, pp.035012
Existence and absence of ground states for a particle interacting through the quantized scalar field on a static spacetime
RIMS Kokyuroku Bessatsu, 2010, B21, pp.015-024
