Theoretical seminars in Kapitza Institute for Physical Problems
Large deviations of surface height in the Kardar-Parisi-Zhang equation
31 May in 11:30
Baruch Meerson (Hebrew University of Jerusalem)
The Kardar-Parisi-Zhang (KPZ) equation describes an important universality class of nonequilibrium stochastic growth. There has been a surge of recent interest in the one-point probability distribution P(H,t) of height H of the evolving interface at time t in one dimension. I will show how one can use the optimal fluctuation method (OFM) to evaluate P(H,t) for different initial conditions and in different dimensions. In one dimension the central part of the short-time height distribution is Gaussian, but the tails are non-Gaussian and strongly asymmetric. One interesting initial condition is an ensemble of Brownian interfaces, where we found a singularity of the large deviation function of the height at a critical value of |H|. This singularity results from a breakdown of mirror symmetry of the optimal path of the system, and it has the character of a second-order phase transition. At d>2 the OFM is valid, in the weak-coupling regime, at all times. Here the long-time height distribution P(H) is time-independent, and we use the OFM to determine the Gaussian body and strongly asymmetric non-Gaussian tails of P(H).
Seminars are held on Thursdays in the conference hall Kapitza Institute for Physical Problems in Moscow, beginning at 11:30.