Transport in the barrier billiard.

We investigate transport properties of an ensemble of particles moving inside an infinite periodic horizontal planar barrier billiard. A particle moves among bars and elastically reflects on them. The motion is a uniform translation along the bars' axis. When the tangent of the incidence angle, α, is fixed and rational, the second moment of the displacement along the orthogonal axis at time n, ã€ˆS_{n}^{2}〉, is either bounded or asymptotic to Kn^{2}, when n→∞. For irrational α, the collision map is ergodic and has a family of weakly mixing observables, the transport is not ballistic, and autocorrelation functions decay only in time average, but may not decay for a family of irrational α's. An exhaustive numerical computation shows that the transport may be superdiffusive or subdiffusive with various rates or bounded strongly depending on the values of α. The variety of transport behaviors sounds reminiscent of well-known behavior of conservative systems. Considering then an ensemble of particles with nonfixed α, the system is nonergodic and certainly not mixing and has anomalous diffusion with self-similar space-time properties. However, we verified that such a system decomposes into ergodic subdynamics breaking self-similarity.

Spin-Glass Model Governs Laser Multiple Filamentation.

We show that multiple filamentation patterns in high-power laser beams can be described by means of two statistical physics concepts, namely, self-similarity of the patterns over two nested scales and nearest-neighbor interactions of classical rotators. The resulting lattice spin model perfectly reproduces the evolution of intense laser pulses as simulated by the nonlinear Schrödinger equation, shedding new light on multiple filamentation. As a side benefit, this approach drastically reduces the computing time by 2 orders of magnitude as compared to the standard simulation methods of laser filamentation.

Laser filamentation as a new phase transition universality class.

We show that the onset of laser multiple filamentation can be described as a critical phenomenon that we characterize both experimentally and numerically by measuring a set of seven critical exponents. This phase transition deviates from any existing universality class and offers a unique perspective of conducting two-dimensional experiments of statistical physics at a human scale.

Reversibility of laser filamentation.

We investigate the reversibility of laser filamentation, a self-sustained, non-linear propagation regime including dissipation and time-retarded effects. We show that even losses related to ionization marginally affect the possibility of reverse propagating ultrashort pulses back to the initial conditions, although they make it prone to finite-distance blow-up susceptible to prevent backward propagation.

Stochastic treatment of finite-N effects in mean-field systems and its application to the lifetimes of coherent structures.

A stochastic treatment yielding to the derivation of a general Fokker-Planck equation is presented to model the slow convergence toward equilibrium of mean-field systems due to finite-N effects. The thermalization process involves notably the disintegration of coherent structures that may sustain out-of-equilibrium quasistationary states. The time evolution of the fraction of particles remaining close to a mean-field potential trough is analytically computed. This indicator enables to estimate the lifetime of coherent structures and thermalization time scale in mean-field systems.

Generalized Miller formulae.

We derive the spectral dependence of the non-linear susceptibility of any order, generalizing the common form of Sellmeier equations. This dependence is fully defined by the knowledge of the linear dispersion of the medium. This finding generalizes the Miller formula to any order of non-linearity. In the frequency-degenerate case, it yields the spectral dependence of non-linear refractive indices of arbitrary order.