Title: Analytic Theory of Non-Gaussian Transport in Disordered Media: Beyond Continuous Time Random Walk
Author: Sanggeun Song
In this study, we introduce an analytic theory of non-Gaussian transport in disordered media based on a nonrenewal continuous time random walk (CTRW) model to describe stochastic transport in dynamically disordered media. In this model, based on the general relationship between jump event counting statistics and CTRW, we used the critical state configuration, which is generally shown in many reactions to account for hidden environments. To explain the general behavior of mean square displacement, we adopt the analytic, applicable expression. The mean square displacement of our model may explain the anomalous transport phenomena frequently observed in heterogeneous environments, which is proportional to time squared at short times, the power-law at intermediate times, and linear dependence at long times. Using the non-Gaussian parameter (NGP), we are able to extract the autocorrelation function of the transition rate. We, additionally, discover that the transition rate autocorrelation function has a peak-shaped profile around the maximum NGP time, reflecting dynamic heterogeneity.