TY - JOUR

T1 - Large fluctuations of a Kardar-Parisi-Zhang interface on a half line

AU - Meerson, Baruch

AU - Vilenkin, Arkady

N1 - Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/9/28

Y1 - 2018/9/28

N2 - Consider a stochastic interface h(x,t), described by the 1+1 Kardar-Parisi-Zhang (KPZ) equation on the half line x≥0. The interface is initially flat, h(x,t=0)=0, and driven by a Neumann boundary condition ∂xh(x=0,t)=A and by the noise. We study the short-time probability distribution PH,A,t of the one-point height H=h(x=0,t). Using the optimal fluctuation method, we show that -lnPH,A,t scales as t-1/2sH,At1/2. For small and moderate |A| this more general scaling reduces to the familiar simple scaling -lnPH,A,t≃t-1/2s(H), where s is independent of A and time and equal to one half of the corresponding large-deviation function for the full-line problem. For large |A| we uncover two asymptotic regimes. At very short time the simple scaling is restored, whereas at intermediate times the scaling remains more general and A-dependent. The distribution tails, however, always exhibit the simple scaling in the leading order.

AB - Consider a stochastic interface h(x,t), described by the 1+1 Kardar-Parisi-Zhang (KPZ) equation on the half line x≥0. The interface is initially flat, h(x,t=0)=0, and driven by a Neumann boundary condition ∂xh(x=0,t)=A and by the noise. We study the short-time probability distribution PH,A,t of the one-point height H=h(x=0,t). Using the optimal fluctuation method, we show that -lnPH,A,t scales as t-1/2sH,At1/2. For small and moderate |A| this more general scaling reduces to the familiar simple scaling -lnPH,A,t≃t-1/2s(H), where s is independent of A and time and equal to one half of the corresponding large-deviation function for the full-line problem. For large |A| we uncover two asymptotic regimes. At very short time the simple scaling is restored, whereas at intermediate times the scaling remains more general and A-dependent. The distribution tails, however, always exhibit the simple scaling in the leading order.

UR - http://www.scopus.com/inward/record.url?scp=85054549751&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.98.032145

DO - 10.1103/PhysRevE.98.032145

M3 - Article

AN - SCOPUS:85054549751

SN - 2470-0045

VL - 98

JO - Physical Review E

JF - Physical Review E

IS - 3

M1 - 032145

ER -