Soft-mode turbulence (SMT) observed in the electroconvection of a nematic liquid crystal is a first experimental example of spatiotemporal chaos (STC) due to an additional Goldstone mode. In a nematic liquid crystal with homeotropic alignment a continuous rotational symmetry is broken by a kind of buckling instability of the alignment by applying voltage (control parameter), and this spontaneous symmetry breaking leads to a Goldstone mode. Further increasing the control parameter, electroconvective instability sets in and a roll pattern could be expected to appear. SMT however ensues by the coupling of the roll pattern with the Goldstone mode. SMT has the following properties: (i) SMT is one of the rare examples of STC appearing via single supercritical bifurcation directly from a quiescent state. With decreasing the control parameter, the correlation time of the chaotic fluctuation becomes longer and diverges at the bifurcation point, that is, the fluctuations become soft, (ii) SMT is the STC in respect to the directions of convective wavevector, and patches which are the areas with the same directions appear, (iii) The averaged size of the patch, as well as the the correlation length, becomes larger with decreasing the control parameter from the above of threshold. Furthermore we have investigated transport properties in SMT by observing non-thermal "Brownian motion" in order to elucidate a fluctuation theorem in dissipative systems. This study gives us important information about SMT from a viewpoint of the Lagrangian picture which is different from the properties of the Euler picture (pattern dynamics). We presented the time-scale dependence of diffusion constants obtained by a coarse-graining. The obtained result reflects that SMT pattern has two different length scales, rolls and patches. The diffusion of particles inside a patch is anomalous, i.e. Lévy diffusion, while the diffusion of inter-patches is normal. Thus the transport property of SMT is closely related with its spatial hierarchy.
!!!All Science Journal Classification (ASJC) codes