TY - JOUR

T1 - Time-averaged height distribution of the Kardar-Parisi-Zhang interface

AU - Smith, Naftali R.

AU - Meerson, Baruch

AU - Vilenkin, Arkady

N1 - Funding Information:
We thank Tal Agranov and Joachim Krug for useful discussions and acknowledge financial support from the Israel Science Foundation (Grant No. 807/16). NRS was supported by the Clore Israel Foundation.
Publisher Copyright:
© 2019 Institute of Physics Publishing. All rights reserved.

PY - 2019/5/30

Y1 - 2019/5/30

N2 - We study the complete probability distribution P H , t of the time-averaged height H = (1/t) t 0 h(x = 0, t) dt at point x = 0 of an evolving 1 + 1 dimensional Kardar Parisi Zhang (KPZ) interface h (x, t). We focus on short times and flat initial condition and employ the optimal fluctuation method to determine the variance and the third cumulant of the distribution, as well as the asymmetric stretched-exponential tails. The tails scale as ?lnP H 3/2 /t and ?lnP H 5/2 /t, similarly to the previously determined tails of the one-point KPZ height statistics at specified time t = t. The optimal interface histories, dominating these tails, are markedly di erent. Remarkably, the optimal history, h (x = 0, t), of the interface height at x = 0 is a non-monotonic function of time: the maximum (or minimum) interface height is achieved at an intermediate time. We also address a more general problem of determining the probability density of observing a given height history of the KPZ interface at point x = 0.

AB - We study the complete probability distribution P H , t of the time-averaged height H = (1/t) t 0 h(x = 0, t) dt at point x = 0 of an evolving 1 + 1 dimensional Kardar Parisi Zhang (KPZ) interface h (x, t). We focus on short times and flat initial condition and employ the optimal fluctuation method to determine the variance and the third cumulant of the distribution, as well as the asymmetric stretched-exponential tails. The tails scale as ?lnP H 3/2 /t and ?lnP H 5/2 /t, similarly to the previously determined tails of the one-point KPZ height statistics at specified time t = t. The optimal interface histories, dominating these tails, are markedly di erent. Remarkably, the optimal history, h (x = 0, t), of the interface height at x = 0 is a non-monotonic function of time: the maximum (or minimum) interface height is achieved at an intermediate time. We also address a more general problem of determining the probability density of observing a given height history of the KPZ interface at point x = 0.

KW - Fluctuation phenomena

KW - Kinetic growth processes

KW - Large deviations in non-equilibrium systems

UR - http://www.scopus.com/inward/record.url?scp=85069531751&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/ab16c1

DO - 10.1088/1742-5468/ab16c1

M3 - Article

AN - SCOPUS:85069531751

SN - 1742-5468

VL - 2019

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 5

M1 - 53207

ER -