Numerical approach to unbiased and driven generalized elastic model

TL;DR

This paper investigates the properties of the generalized elastic model (GEM) through scaling arguments and numerical simulations, focusing on subdiffusion, ergodicity, and driven dynamics in physical systems like polymers and membranes.

Contribution

It provides a comprehensive numerical analysis of the GEM, including subdiffusion exponents, fluctuation scaling, ergodic behavior, and driven responses, offering new insights into its physical properties.

Findings

Subdiffusion exponent matches analytical predictions

Interface fluctuations show no intermittent behavior

Driven GEM exhibits characteristic drift behavior

Abstract

From scaling arguments and numerical simulations, we investigate the properties of the generalized elastic model (GEM), that is used to describe various physical systems such as polymers, membranes, single-file systems, or rough interfaces. We compare analytical and numerical results for the subdiffusion exponent beta characterizing the growth of the mean squared displacement <(delta h)^2> of the field h described by the GEM dynamic equation. We study the scaling properties of the qth order moments <|delta h|^q> with time, finding that the interface fluctuations show no intermittent behavior. We also investigate the ergodic properties of the process h in terms of the ergodicity breaking parameter and the distribution of the time averaged mean squared displacement. Finally, we study numerically the driven GEM with a constant, localized perturbation and extract the characteristics of the average drift for a tagged probe.