Langevin picture of subdiffusive particles under the joint influence of an expanding medium and an external constant force

It has been found that expanding medium has a nonnegligible influence on particle's diffusion, the physical mechanism of which is quite different from an external force field. To study the joint influence of the expanding medium and the constant force, we start from the Langevin picture of the subdiffusive particles in the expanding medium, and then introduce the effect of the external constant force in two ways, which are sustainedly or intermittently acting on the particle's motion. Therefore, we get two models with the only difference on the force terms. Then under the framework of the Langevin equation, we conduct detailed analyses and derive the corresponding Fokker-Planck equations and the moments for the two models. In the case with the sustained constant force, the force behaves as a decoupled force, which is called Galilei invariant. While for the intermittent case, the force changes the diffusion behavior, and the specific effects vary according to the expanding rate of the medium. Our detailed theoretical analyses and simulations present a consistent Langevin framework of investigating anomalous diffusion phenomena in the expanding medium together with the external force.

Automated summary

This article investigates the joint influence of expanding medium and constant force on particle diffusion. By starting from the Langevin picture and introducing the effect of external force in two different ways, two models with different force terms are obtained. Detailed analysis and derivation yield the Fokker-Planck equations and moments for the two models. The sustained force behaves as a decoupled force, while the intermittent force changes the diffusion behavior with specific effects depending on the expanding rate of the medium.