CRM: Centro De Giorgi
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Probabilistic methods in statistical physics for extreme statistics and rare events

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

speaker: Naftali Smith (Hebrew university in Jerusalem)

abstract: We study the short-time distribution \( \mathcal{P}\left(H,L,t\right) \) of the two-point two-time height difference \( H=h(L,t)-h(0,0) \) of a stationary Kardar-Parisi-Zhang (KPZ) 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 \( H=H_c \). 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 \( \mathcal{P}\left(H,L,t\right) \) in several limits away from the second-order transition. Typical fluctuations of \( H \) are Gaussian, but the distribution tails are highly asymmetric. The tails \( -\ln\mathcal{P}\sim\left
H\right
^{3/2} \! /\sqrt{t} \) and \( -\ln\mathcal{P}\sim\left
H\right
^{5/2} \! /\sqrt{t} \), previously found for \( L=0 \), are enhanced for \( L \ne 0 \). At very large \(
L
\) the whole height-difference distribution \( \mathcal{P}\left(H,L,t\right) \) is time-independent and Gaussian in \( H \), \( -\ln\mathcal{P}\sim\left
H\right
^{2} \! /
L
\), describing the probability of creating a ramp-like height profile at \( t=0 \).


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