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 |
Equivalence of definitions of solutions for some class of fractional diffusion equations
Mathematical News / Mathematische Nachrichten, 2023, 296 (12), pp.5617-5645. (10.1002/mana.202100617)
Inverse source problem with a posteriori boundary measurement for fractional diffusion equations
Mathematical Methods in the Applied Sciences, 2023, 46 (14), pp.15868-15882. (10.1002/mma.9432)
Global recovery of a time-dependent coefficient for the wave equation from a single measurement
Asymptotic Analysis, 2023, 131 (3-4), pp.513-539. (10.3233/ASY-221779)
Recovery of Nonlinear Terms for Reaction Diffusion Equations from Boundary Measurements
Archive for Rational Mechanics and Analysis, 2023, 247 (1), pp.6. (10.1007/s00205-022-01831-y)
Lipschitz and Hölder stable determination of nonlinear terms for elliptic equations
Nonlinearity, 2023, 36 (2), pp.1302-1322. (10.1088/1361-6544/acafcd)
On the Dirac bag model in strong magnetic fields
Pure and Applied Analysis, In press, 5 (3), pp.643-727. (10.2140/paa.2023.5.643)
The enclosure method for the detection of variable order in fractional diffusion equations
Inverse Problems and Imaging , 2023, 17 (1), pp.180-202. (10.3934/ipi.2022036)
Maximal regularity for semilinear non-autonomous evolution equations in temporally weighted spaces
Arabian Journal of Mathematics, 2022, 11 (3), pp.539-547. (10.1007/s40065-022-00390-0)
An inverse problem for a quasilinear convection–diffusion equation
Nonlinear Analysis: Theory, Methods and Applications, 2022, 222, pp.112921. (10.1016/j.na.2022.112921)
The one dimensional semi-classical Bogoliubov-de Gennes Hamiltonian
2022
