Laboratoire Matière et Systèmes Complexes

Exploring universal out-of-equilibrium scaling laws with turbulent liquid crystal

Kazumasa A. Takeuchi (Univ. of Tokyo)

To what extent can scale-invariant phenomena out of equilibrium be described by universal scaling laws ? Apart from few examples such as developed turbulence, experimental studies in this context are usually hampered by limited system size and complex interactions of the systems, which make them difficult to be compared with theoretical developments. Here, I show that chaotic convection of electrically driven nematic liquid crystal is an ideal system to overcome such difficulties, which allows for thorough experimental tests of out-of-equilibrium scaling laws and beyond.

First we study a route to turbulence in this electroconvection, focusing on the transition between two regimes of spatiotemporal chaos via spatiotemporal intermittency. Measuring both static and dynamic critical behavior, we identify the directed percolation universality class, which is theoretically known as the most fundamental class for absorbing-state phase transitions.

We then study interface dynamics of growing turbulent domains under high applied voltage, which turns out to be in the Kardar-Parisi-Zhang (KPZ) class, a prototypical class for stochastic growing interfaces. Remarkably, interface fluctuations are found to exhibit particular distributions developed in random matrix theory, which arise as universal properties of the KPZ-class interfaces. The experiment illustrates that the KPZ class splits into a few subclasses depending on the global shape of the interfaces, revealing a number of characteristic properties that remain to be explained theoretically.