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 |
Some Remarks on Spectral Averaging and the Local Density of States for Random Schrödinger Operators on $L^2 (\mathbb {R}^d)$
Schrödinger Operators, Spectral Analysis and Number Theory, 348, pp.117-132, 2021, Springer Proceedings in Mathematics & Statistics, 978-3-030-68489-1. (10.1007/978-3-030-68490-7_6)
The inverse problem of two-state quantum systems with non-adiabatic static linear coupling
Communications in Contemporary Mathematics, 2021, 23 (04), pp.2050002. (10.1142/S0219199720500029)
Large deviations and entropy production in viscous fluid flows
Archive for Rational Mechanics and Analysis, 2021, 240 (3), pp.1675-1725. (10.1007/s00205-021-01646-3)
On semi-classical spectral series for an atom in a periodic polarized electric field
Days of Diffraction 2021, May 2021, Saint Petersbourg, Russia
Unique determination of several coefficients in a fractional diffusion(-wave) equation by a single measurement
2021
Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations
Fractional Calculus and Applied Analysis, 2021, 24 (1), pp.168-201. (10.1515/fca-2021-0008)
Semiclassical Green functions and Lagrangian intersection. Applications to the propagation of Bessel beams in non-homogeneous media
2021
On the determination of nonlinear terms appearing in semilinear hyperbolic equations
Journal of the London Mathematical Society, 2021, 104 (2), pp.572-595. (10.1112/jlms.12440)
On the semiclassical spectrum of the Dirichlet-Pauli operator
Journal of the European Mathematical Society, 2021, 23 (10), pp.3279-3321. (10.4171/JEMS/1085)
The uniqueness of inverse problems for a fractional equation with a single measurement
Mathematische Annalen, 2021, 380 (3-4), pp.1465-1495. (10.1007/s00208-020-02027-z)
