title: Dynamical phase transition in large-deviation statistics of the Kardar-Parisi-Zhang equation.
abstract: We study the short-time behavior of the probability distribution P(H,t) of the surface height h(x=0,t)=H in the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension. The process starts from a stationary interface: h(x,t=0) is given by a realization of two-sided Brownian motion constrained by h(0,0)=0. We find a singularity of the large deviation function of H at a critical value H=H_{c}. The singularity has the character of a second-order phase transition. It reflects spontaneous breaking of the reflection symmetry x↔-x of optimal paths h(x,t) predicted by the weak-noise theory of the KPZ equation. At |H|≫|H_{c}| the corresponding tail of P(H) scales as -lnP∼|H|^{3/2}/t^{1/2} and agrees, at any t>0, with the proper tail of the Baik-Rains distribution, previously observed only at long times. The other tail of P scales as -lnP∼|H|^{5/2}/t^{1/2} and coincides with the corresponding tail for the sharp-wedge initial condition.
authors.affiliation: Department of Physics, University of Minnesota, Minneapolis, Minnesota 55455, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Janas
authors.affiliation: Department of Physics, University of Minnesota, Minneapolis, Minnesota 55455, USA.|William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA.
authors.forename: Alex
authors.initials: A
authors.lastname: Kamenev
authors.affiliation: Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
authors.forename: Baruch
authors.initials: B
authors.lastname: Meerson