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 source problems in elastodynamics
Inverse Problems, 2018, 34 (4), pp.045009. (10.1088/1361-6420/aaaf7e)
A mathematical account of the NEGF formalism
Annales Henri Poincaré, 2018, 19 (2), pp.411-442. (10.1007/s00023-017-0638-2)
Determination of singular time-dependent coefficients for wave equations from full and partial data
Inverse Problems and Imaging , 2018, 12 (3), pp.745-772. (10.3934/ipi.2018032)
A multidimensional Borg-Levinson theorem for magnetic Schrödinger operators with partial spectral data
Journal of Spectral Theory, 2018, 8 (1), pp.235-269. (10.4171/JST/195)
Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term
Journal de Mathématiques Pures et Appliquées, 2018, 114, pp.235-261. (10.1016/j.matpur.2017.12.003)
Global uniqueness in an inverse problem for time fractional diffusion equations
Journal of Differential Equations, 2018, 264 (2), pp.1146-1170. (10.1016/j.jde.2017.09.032)
Stability result for elliptic inverse periodic coefficient problem by partial Dirichlet-to-Neumann map
Journal of Spectral Theory, 2018, 8 (2), pp.733-768. (10.4171/JST/212)
Bohr-Sommerfeld Quantization Rules Revisited: The Method of Positive Commutators
Journal of Mathematical Sciences the University of Tokyo, In press, J. Math. Sci. Univ. Tokyo, 25, p.91-137
An inverse problem for the magnetic Schrödinger equation in infinite cylindrical domains
Publications of the Research Institute for Mathematical Sciences, 2018, 54 (4), pp.679-728. (10.4171/PRIMS/54-4-1)
On Time-Fractional Diffusion Equations with Space-Dependent Variable Order
Annales Henri Poincaré, 2018, 19 (12), pp.3855-3881. (10.1007/s00023-018-0734-y)
