Explaining the statistical physics of growing liquid crystal interfaces with the KPZ equation: Part I
Systems at the critical point become scale-invariant and so are, in many cases, successfully described by the stochastic motion of a point (i.e Brownian motion) which reflects this scale invariance and resulting universal features such as Gaussian fluctuations. Similarly the stochastic motion of a line is also scale-invariant, and so can be used to model natural processes such as the growth of interfaces. Experiments, published in 2011, of the growing interfaces of liquid crystal turbulence found that the interface positions have universal distributions. These universal distributions are described theoretically by the Kardar-Parisi-Zhang (KPZ) equation, which was developed to describe interface growth.
In this talk, I will very simply describe how an interacting 1-dimensional model of random walkers - known as the Antisymmetric Simple Exclusion Process (ASEP) - is equivalent to a model of interfacial growth, and that the KPZ equation can be straightforwardly derived from its fluctuating hydrodynamics. I will also present how some information about the large scale fluctuations of the KPZ equation can be derived, in particular the universal exponent of the height fluctuations of the interface. In general, I would like to convey how a remarkable amount of theoretical work culminated with some intricate experimental results that completely corresponded to the theory.
I want to emphasise that although there will be technical details, all of the mathematics will be very accessible - no prior knowledge assumed!
This is a roughly weekly series of didactical blackboard talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..