Time-dependent correlation functions in systems with interactions and surface diffusion measurements

Abstract

Different surface diffusion coefficients are measured from the time dependence of different statistical quantities such as the mean square displacement R 2, and the correlation function C( t) of concentration fluctuations within a probe region. For non-interacting systems, R 2 grows linearly with time and C( t) has the characteristic 1 (Dt) tail in the long time regime. We have performed Monte Carlo simulations on a lattice gas model with nearest-neighbor repulsive interactions at coverage υ = 0.5, over a wide temperature range ( T T c > 0.7 ) to test whether these expressions also hold in systems with interactions. We find that R 2 still grows linearly with time but the single site correlation function C s ( t) deviates from the non-interacting form. No 1 (Dt) tails are observed within the range of a measurable signal in the decay of C s ( t) when the temperature is within the ordered region T T c < 1 . The form of C s ( t) is relevant for a newly developed method that analyses the time dependence of the STM current fluctuations to measure the collective diffusion coefficient.