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 emeritus | +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 emeritus | +33.4.91.26.97.97 | Contact |
| SOCCORSI | Eric | Research teacher | +33.4.91.26.95.37 | Contact |
The second critical point for the Perfect Bose gas in quasi-one-dimensional traps
2010
The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory
Matematicheskie Zametki / Mathematical Notes, 2010, 87 (3), pp.430-435. (10.1134/S0001434610030168)
The second critical density and generalised condensation
Condensed Matter Physics, 2010, 13 (2), pp.23003. (10.5488/CMP.13.23003)
Existence and absence of ground states for a particle interacting through the quantized scalar field on a static spacetime
RIMS Kokyuroku Bessatsu, 2010, B21, pp.015-024
Simultaneous Identification of the Diffusion Coefficient and the Potential for the Schrôdinger Operator with one Observation
Inverse Problems, 2010, 26, pp.035012
Hydrogenic systems confined by infinite tubes
Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), pp.474018. (10.1088/1751-8113/43/47/474018)
General algorithm of computation of c-table and detection of valleys
Ukrainian Mathematical Journal, 2010, 62 (6), pp.882-893. (10.1007/s11253-010-0397-4)
Asymptotic behaviours and general recurrence relations
Applied Numerical Mathematics: an IMACS journal, 2010, 60 (12), pp.1352-1363. (10.1016/j.apnum.2010.08.001)
On the relation between measures defining the Stieltjes and the inverted Stieltjes functions
Ukrainian Mathematical Journal, 2010, 62 (3), pp.373-379. (10.1007/s11253-010-0360-4)
Diamagnetism of quantum gases with singular potentials
Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), pp.474008. (10.1088/1751-8113/43/47/474008)
