Generalized survival in equilibrium step fluctuations

TL;DR

This paper studies a generalized survival probability in equilibrium step fluctuations, revealing its exponential decay and scaling behavior with system size, sampling time, and reference level, with the survival time scale decreasing exponentially with the reference level.

Contribution

It introduces and analyzes a generalized survival probability with respect to an arbitrary reference level in equilibrium step fluctuations, highlighting its scaling properties and exponential decay behavior.

Findings

$S(t,R)$ exhibits simple scaling with system size, sampling time, and reference level.

The generalized survival time scale $ au_s(R)$ decays exponentially with $R$.

Numerical analysis confirms the exponential decay at large time scales.

Abstract

We investigate the dynamics of a generalized survival probability $S(t,R)$ defined with respect to an arbitrary reference level $R$ (rather than the average) in equilibrium step fluctuations. The exponential decay at large time scales of the generalized survival probability is numerically analyzed. $S(t,R)$ is shown to exhibit simple scaling behavior as a function of system-size $L$, sampling time $\delta t$, and the reference level $R$. The generalized survival time scale, $\tau_s(R)$, associated with $S(t,R)$ is shown to decay exponentially as a function of $R$.