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 |
Entropic Fluctuation Theorems for the Spin-Fermion Model
Journal of Mathematical Physics, 2026, 67 (2), (10.1063/5.0311182)
Inverse Coefficient Problem for One-Dimensional Subdiffusion with Data on Disjoint Sets in Time
Communications in Mathematical Sciences, 2026, 24, pp.645-661
Green's functions for magnetic Dirac operators and bulk-edge correspondence
2025
Geometric spectral properties of electromagnetic waveguides
2025
Entropic Fluctuations in Statistical Mechanics II. Quantum Dynamical Systems
Communications in Mathematical Physics, 2025, pp.406:201. (10.1007/s00220-025-05360-z)
Stability analysis of inverse problems for coupled magnetic Schrödinger equations
Inverse Problems, 2025, 41 (3), pp.035009. (10.1088/1361-6420/adb2bc)
On time-fractional partial differential equations of time-dependent piecewise constant order
Mathematical Methods in the Applied Sciences, 2025, 48 (2), pp.2354-2369. (10.1002/mma.10439)
RENORMALIZATION OF GENERALIZED SPIN-BOSON MODELS WITH CRITICAL ULTRAVIOLET DIVERGENCES
2025
What is the absolutely continuous spectrum?
2024
Edge currents for the time-fractional, half-plane, Schrödinger equation with constant magnetic field
Journal of Mathematical Physics, 2024, 65 (10), (10.1063/5.0198112)
