Diffusion on a lattice: Transition rates, interactions, and memory effects

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• Particle diffusion on lattices is fundamental to transport phenomena.
• Interactions within lattice sites influence macroscopic diffusion properties.
• Previous work derived transition rates based on excess chemical potential.

Purpose of the Study:

• To derive an approximate expression for the correlation factor (f) in tracer diffusivity.
• To analyze the impact of memory effects on particle diffusion.
• To apply the derived expression to soft-core and extended hard-core interactions.

Main Methods:

• Analysis of particle diffusion on a two-dimensional square lattice.
• Utilizing a general expression for transition rates dependent on excess chemical potential.
• Deriving the mean-field tracer diffusivity (D^MF).
• Analyzing joint probability distributions to approximate the correlation factor (f).

Main Results:

• An approximate expression for the correlation factor (f) was derived.
• Tracer diffusivity (D) was expressed as D = D^MF * f, incorporating memory effects.
• The derived expression was successfully applied to soft-core and extended hard-core interaction models.

Conclusions:

• The correlation factor (f) provides crucial insights into memory effects in lattice diffusion.
• The derived expression offers a method to quantify these memory effects for various interaction potentials.
• This work advances the understanding of diffusion in interacting particle systems on lattices.