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 |
Estimates On The Molecular Dynamics For The Predissociation Process
Journal of Spectral Theory, 2017, 7 (2), pp.487-517. (10.4171/JST/170)
Stability result for two coefficients in a coupled hyperbolic-parabolic system
Journal of Inverse and Ill-posed Problems, 2017, 25 (3), (10.1515/jiip-2015-0017)
Twisted waveguide with a Neumann window
Functional Analysis and Operator Theory for Quantum Physics : The Pavel Exner Anniversary Volume, European Mathematical Society, pp.161-175, 2017, EMS Series of Congress Reports, 978-3-03719-175-0. (10.4171/175-1/8)
Règles de quantification semi-classique pour une orbite périodique de type hyberbolique
Mathématiques générales [math.GM]. Université de Toulon; Université de Tunis El-Manar. Faculté des Sciences de Tunis (Tunisie), 2017. Français. (NNT : 2017TOUL0004)
Quantum Vorticity at positive temperature for spin systems with continuous symmetry
Journal of Physics: Conference Series, 2017, ISQS24, Int. Conference on Integrable Syst. and Quantum symmetries, 804 (1), pp.012031. (10.1088/1742-6596/804/1/012031)
On the well posedness of the magnetic Schrödinger-Poisson system in $R^3$
Mathematical Modelling of Natural Phenomena, 2017, 12 (1), pp.15 - 22. (10.1051/mmnp/201712102)
On Existence and Uniqueness of Solutions for Semilinear Fractional Wave Equations
Fractional Calculus and Applied Analysis, 2017, 20 (1), pp.117-138. (10.1515/fca-2017-0006)
Unique determination of a time-dependent potential for wave equations from partial data
Annales de l'Institut Henri Poincaré (C), Analyse non linéaire (Nonlinear Analysis), 2017, 34 (4), pp.973-990. (10.1016/j.anihpc.2016.07.003)
Spectral theory near thresholds for weak interactions with massive particles
Journal of Spectral Theory, 2016, 6 (3), pp.505-555. (10.4171/JST/131)
Existence and nonlinear stability of stationary states for the magnetic Schrödinger-Poisson system
Journal of Mathematical Sciences, 2016, 219 (6), pp.874-898. (10.1007/s10958-016-3152-z)
