Group “Classical and Quantum Dynamical Systems”
Statistical properties of dynamical systems: Probabilistic methods are used to study limit theorems in the case of deterministic and random dynamical systems, in particular the Central Limit Theorem (CLT), the Almost Sure Invariance Principle, large deviations, and the distribution of rare events. The rate of decay of correlations for non-uniformly hyperbolic systems is estimated using new techniques (coupling, renewal). Random systems (by random composition of mappings acting on the same space) and sequential dynamical systems (non-stationary or non-autonomous, where a concatenation of mappings acts on a space) are also studied. We have formulated and developed the theory of extreme values for random and non-autonomous systems, with extensions to networks of coupled mappings.
Fusion plasma physics: We develop reduced fluid and kinetic Hamiltonian models derived from Dirac’s constraint theory to study the fundamental mechanisms of turbulent magnetized plasmas that degrade confinement in tokamak devices. Parasitic instabilities in a hybrid non-Hamiltonian model for the interaction of energetic particles with a thermal plasma are also studied, as well as secondary instabilities following magnetic reconnection. Another part of the research activity concerns the application of stochastic process theory to study the formation of transport barriers in tokamaks.
Biophysics: We focus on fundamental physical processes, in particular resonant electrodynamic forces acting over long distances, which are thought to be responsible for the high efficiency of molecular machinery within living cells and for long-range coherence in biological systems. This activity is pursued both theoretically and experimentally in collaboration with molecular biologists.
Complexity: New methods for measuring the complexity of networks are developed within the framework of Riemannian Information Geometry. Applications to networks of proteomic interactions in cancer cells are currently being developed.
| ASCH | Joachim | Research teacher | +33.4.91.26.95.20 | Contact |
| ASCHBACHER | Walter | Research teacher | +33.4.91.26.95.16 | Contact |
| DAQUIN | Jerome | Research teacher | Contact | |
| EL KETTANI | Perla | Research teacher Unit leader « Systèmes dynamiques classiques et quantiques » | +33.4.91.26.97.93 | Contact |
| FLORIANI | Elena | Research teacher | +33.4.91.26.95.22 | Contact |
| LEBOUAZDA | Yohann | Ph.D. | Contact | |
| LEONCINI | Xavier | Research teacher Team leader « Dynamical Systems: Theory and Applications » | +33.4.91.26.95.38 | Contact |
| PETTINI | Marco | Research teacher | +33.4.91.26.95.49 | Contact |
| ROUVET | Simon | Ph.D. | Contact | |
| VAIENTI | Sandro | Research teacher | +33.4.91.26.95.44 | Contact |
| VITTOT | Michel | Researcher | +33.4.91.26.95.24 | Contact |
Almost sure invariance principle for random piecewise expanding maps
Nonlinearity, 2018, 31 (5), pp.2252. (10.1088/1361-6544/aaaf4b)
Topological origin of phase transitions in the absence of critical points of the energy landscape
Journal of Statistical Mechanics: Theory and Experiment, 2018, 2018, pp.093204. (10.1088/1742-5468/aad6b6)
A spectral approach for quenched limit theorems for random expanding dynamical systems
Communications in Mathematical Physics, 2018, 360 (3), pp.1121-1187. (10.1007/s00220-017-3083-7)
Extreme Value Laws for Sequences of Intermittent Maps
Proceedings of the American Mathematical Society, 2018, 146 (5), pp.2103-2116. (10.1090/proc/13892)
Correlation dimension and phase space contraction via extreme value theory
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2018, 28 (4), pp.041103. (10.1063/1.5027386)
Long-range electrodynamic interactions among biomolecules
Biological Physics [physics.bio-ph]. Aix-Marseille Université, 2017. English. (NNT : )
Théorèmes limites dans l'analyse statistique des systèmes dynamiques
Mathématiques générales [math.GM]. Université de Toulon; Université de Sfax. Faculté des sciences, 2017. Français. (NNT : 2017TOUL0010)
Hamiltonian closures in fluid models for plasmas
The European Physical Journal D : Atomic, molecular, optical and plasma physics, 2017, 71 (11), pp.269. (10.1140/epjd/e2017-80223-6)
Stability criterion of spatially inhomogeneous solutions to the Vlasov equation
Journal of Physics A: Mathematical and Theoretical, 2017, 50 (45), pp.455001. (10.1088/1751-8121/aa8dbb)
Detection of long-range electrostatic interactions between charged molecules by means of fluorescence correlation spectroscopy
Physical Review E , 2017, 96 (2), pp.022403 (10.1103/PhysRevE.96.022403)
