Landau theory of the short-time dynamical phase transitions of the Kardar-Parisi-Zhang interface

We study the short-time distribution PH,L,t of the two-point two-time height difference H=h(L,t)-h(0,0) of a stationary Kardar-Parisi-Zhang interface in 1+1 dimension. Employing the optimal-fluctuation method, we develop an effective Landau theory for the second-order dynamical phase transition found previously for L=0 at a critical value H=Hc. We show that |H| and L play the roles of inverse temperature and external magnetic field, respectively. In particular, we find a first-order dynamical phase transition when L changes sign, at supercritical H. We also determine analytically PH,L,t in several limits away from the second-order transition. Typical fluctuations of H are Gaussian, but the distribution tails are highly asymmetric. The tails -lnP∼H3/2/t and -lnP∼H5/2/t, previously found for L=0, are enhanced for L≠0. At very large |L| the whole height-difference distribution PH,L,t is time-independent and Gaussian in H, -lnP∼H2/|L|, describing the probability of creating a ramplike height profile at t=0.