Research

My PhD subject is about noise-induced escape in noisy maps.

Maps are dynamical systems evolving at discrete time. In such systems, instead of a function of the time x(t) describing the state of the system at time t, it is a variable x_n that describe the state of the system at the discrete time n. The evolution of these variables is then ruled by the map x_n+1 = f(x_n). The logistic map x_n+1 = μ x_n (1 - x_n) is a famous example of map depending on one parameter μ.

Noisy maps are maps with the addition of noise : random variables ξ_n that reproduce a pertubation of the maps.
A great number of mesoscopic systems can be modeled by noisy maps, especially because maps are known to exhibit a wide range of behaviors, such as attractors, non-linear bifurcations and chaotic time evolutions. In such models, the noise-induced escape from attractors is a crucial feature and a temporal property such as the mean first exit time is of great importance. In my research, I focus on the weak noise amplitude limit for which a semiclassical formulation of the problem exist in term of a path integral, yielding an Hamiltonian deterministic map at the first order. In this formulation, know as the "symplectic approach" (because the Hamiltonian map have an underlying symplectic structure), the calculation of quantities of the deterministic map allows to estimate the mean first exit time.
My interest is to better understand how this connection between averaged and deterministic quantities occur. I'm also interested about how this approach can be applied to spacialy extended systems and to real-life systems : in the first case to compute kinetic properties and in the latter case to confront theory and experiment.