Nonlinear transport and anomalous Brownian motion in soft-mode turbulence

Soft-mode turbulence (SMT) is a recently discovered type of spatiotemporal chaos observed in the electrohydrodynamic instability (EHD) of a nematic liquid crystal with homeotropic alignment. Its novelty is that it occurs as the first supercritical bifurcation from a stable stationary state in the weakly nonlinear regime of EHD. A particle, small compared to the characteristic length of the macroscopic flow, injected in SMT travels, with random velocity similar to a particle in Brownian motion. We find that the particle trajectory exhibits anomalous Brownian motion such as pumped flight and that the macroscopic diffusion constant due to weak turbulence is about 10³ times larger than the diffusion constant associated with the rest state. The stochastic properties of SMT are discussed.