Step fluctuations and random walks

TL;DR

This paper exactly enumerates the return probability distribution of an atom to a step, analyzing how various factors influence step fluctuations, and uses Monte Carlo simulations to compare with existing theoretical and experimental results.

Contribution

It provides an exact enumeration of return probabilities and explores the effects of step roughness, defects, and interactions on step fluctuations using Monte Carlo methods.

Findings

Return probability distribution p(l) is exactly enumerated.

Monte Carlo simulations match previous theoretical and experimental results.

Step fluctuations depend on roughness, defects, and interactions.

Abstract

The probability distribution p(l) of an atom to return to a step at distance l from the detachment site, with a random walk in between, is exactly enumerated. In particular, we study the dependence of p(l) on step roughness, presence of other reflecting or absorbing steps, interaction between steps and diffusing atom, as well as concentration of defects on the terrace neighbouring the step. Applying Monte Carlo techniques, the time evolution of equilibrium step fluctuations is computed for specific forms of return probabilities. Results are compared to previous theoretical and experimental findings.