Collective transport of Lennard–Jones particles through one-dimensional periodic potentials

The surrounding media in which transport occurs contains various kinds of fields, such as particle potentials and external potentials. One of the important questions is how elements work and how position and momentum are redistributed in the diffusion under these conditions. For enriching Fick's law, ordinary non-equilibrium statistical physics can be used to understand the complex process. This study attempts to discuss particle transport in the one-dimensional channel under external potential fields. Two kinds of potentials–-the potential well and barrier–-which do not change the potential in total, are built during the diffusion process. There are quite distinct phenomena because of the different one-dimensional periodic potentials. By the combination of a Monte Carlo method and molecular dynamics, we meticulously explore why an external potential field impacts transport by the subsection and statistical method. Besides, one piece of evidence of the Maxwell velocity distribution is confirmed under the assumption of local equilibrium. The simple model is based on the key concept that relates the flux to sectional statistics of position and momentum and could be referenced in similar transport problems.