Diffusion of tagged particle in an exclusion process

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Mathematical Physics

Background:

• Understanding particle diffusion is crucial in various scientific fields.
• Classical models often simplify systems, neglecting complex interactions and external forces.
• Hard-core interacting Brownian particles present a challenging system for diffusion studies.

Purpose of the Study:

• To develop a general framework for studying the diffusion of tagged hard-core interacting Brownian particles in one dimension under an external force field.
• To simplify a many-particle diffusion problem into a tractable single-particle problem.
• To derive general equations for particle distribution and mean-square displacement.

Main Methods:

• Utilized the Jepsen line to map the many-particle diffusion problem onto a single-particle problem.
• Derived general equations for particle distribution and mean-square displacement.
• Investigated the specific case of symmetric initial conditions and potential fields.

Main Results:

• Obtained general equations for the distribution and mean-square displacement <(xT)2> of a tagged particle.
• Derived a formula for mean-square displacement: <(xT)2>=R(1-R)/2Nr2 for symmetric cases, where R is the reflection coefficient and r is the non-interacting particle density.
• Demonstrated the applicability of the method to non-Brownian motion and derived the Percus relation for non-Gaussian diffusion.

Conclusions:

• The Jepsen line mapping provides a powerful tool to analyze complex diffusion systems.
• The derived equations are valid for general force fields and initial conditions, offering insights into various physical behaviors.
• This work reveals diffusion behaviors distinct from classical single-file subdiffusion, applicable even for non-Brownian motion.