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 |
Local Wegner and Lifshitz tails estimates for the density of states for continuous random Schrödinger operators
Journal of Mathematical Physics, 2014, 55 (8), pp.083523. (10.1063/1.4893337)
Carleman estimate for infinite cylindrical quantum domains and application to inverse problems
Inverse Problems, 2014, 30 (5), pp.055016. (10.1088/0266-5611/30/5/055016)
Scattering through a straight quantum waveguide with combined boundary conditions
Journal of Mathematical Physics, 2014, 55, pp.112104. (10.1063/1.4901547)
SCATTERING IN TWISTED WAVEGUIDES
Journal of Functional Analysis, 2014, 266 (1), pp.1-35. (10.1016/j.jfa.2013.09.026)
Ground Energy of the Magnetic Laplacian in Polyhedral Bodies
2013
Hyperbolic Hamiltonian flows and the semi-classical Poincaré map
Days on Diffraction 2013, May 2013, St. Petersburg, Russia. pp.53 - 58, (10.1109/DD.2013.6712803)
Determining the implied volatility in the Dupire equation for vanilla European call options
2013
Contribution of the spin-Zeeman term to the binding energy for hydrogen in non-relativistic QED
Annals of the University of Bucharest. Mathematical series, 2013, 4 (LXII), pp.323-336
Computation of the c-Table Related to the Padé Approximation
Journal of Applied Mathematics, 2013, 2013, pp.185648. (10.1155/2013/185648)
Stability of the determination of a time-dependent coefficient in parabolic equations
Mathematical Control and Related Fields, 2013, 3 (2), pp.143-160. (10.3934/mcrf.2013.3.143)
