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 |
Multidimensional tunneling between potential wells at non degenerate minima
Days on Diffraction 2014, May 2014, St. Petersburg, Russia. pp.17-22, (10.1109/DD.2014.7036416)
Inverse problem for a transport equation using Carleman estimates
Applicable Analysis, 2014, 93 (5)
Ground state energy of the magnetic Laplacian on general three-dimensional corner domains
2014
Controllability to trajectories for some parabolic systems of three and two equations by one control force
Mathematical Control and Related Fields, 2014, 4 (1)
Edge currents and eigenvalue estimates for magnetic barrier Schrödinger operators
Asymptotic Analysis, 2014, 89 (3-4), pp.331-363. (10.3233/ASY-141234)
Quantitative Estimates on the Binding Energy for Hydrogen in Non-Relativistic QED. II. The spin case
Reviews in Mathematical Physics, 2014, 26 (8), pp.1450016. (10.1142/S0129055X14500160)
A note on reflectionless Jacobi matrices
Communications in Mathematical Physics, 2014, 332 (2), pp.827-838. (10.1007/s00220-014-2065-2)
Erratum to “Poisson statistics for eigenvalues of continuum random Schrödinger operators”
Analysis & PDE, 2014, 7 (5), pp.1235-1236. (10.2140/apde.2014.7.1235)
Approximation of Smooth Functions by Weighted Means of N-Point Padé Approximants
Ukrainian Mathematical Journal, 2014, 65 (10), pp.1566-1576. (10.1007/s11253-014-0878-y)
Determining the scalar potential in a periodic quantum waveguide from the DN map
Springer-INDAM. New Prospects in Direct, Inverse and Control Problems for Evolution Equations, pp.93-105, 2014, 978-3-319-11406-4
