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 |
Schrödinger operator in the limit of shrinking wave-guide cross section and singularity scaled twisting
2011
Lifshitz tails estimate for the density of states of the Anderson model
Spectra of Random Operators and Related Topics, Jul 2011, Kyoto University, Japan. pp.1-9
Andreev reflection and the semiclassical Bogoliubov-de Gennes Hamiltonian: Resonant states
Days on Diffraction 2011, May 2011, St. Petersburg Russia. pp.39-44, (10.1109/DD.2011.6094362)
On the transfer matrix of a MIMO system
Mathematical Methods in the Applied Sciences, 2011, 34 (8), pp.963-976. (10.1002/mma.1415)
Compatibility of Continued Fraction Convergents with Padé Approximants
Walter Gautschi; Giuseppe Mastroianni; Themistocles M. Rassias. Approximation and Computation: In Honor of Gradimir V. Milovanovi, 42, Springer, pp.135-144, 2011, Springer Optimization and Its Applications, 978-1-4419-6593-6. (10.1007/978-1-4419-6594-3_10)
The semi-classical Maupertuis–Jacobi correspondence for quasi-periodic Hamiltonian flows with applications to linear water waves theory
Asymptotic Analysis, 2011, 74 (1-2), pp.33-73. (10.3233/ASY-2011-1045)
Stability estimate in an inverse problem for non-autonomous Schrödinger equations
Applicable Analysis, 2011, 90 (10), pp.1499-1520
Spectral theory for a mathematical model of the weak interaction: The decay of the intermediate vector bosons W±, II
Annales Henri Poincaré, 2011, 12 (8), pp.1539-1570. (10.1007/s00023-011-0114-3)
H2 MOLECULE IN STRONG MAGNETIC FIELDS
Journal of Physics A: Mathematical and Theoretical, 2010, 43, pp.474005. (10.1088/1751-8113/43/47/474005)
Non analyticity of the ground state energy of the Hamiltonian for Hydrogen atom in nonrelativistic QED
Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), pp.474004. (10.1088/1751-8113/43/47/474004)
