Single-file diffusion · Particle mass
Particle Mass Changes Single-File Diffusion
Main claim
In a one-dimensional file where particles cannot pass, a sufficiently light tracer shows non-Gaussian subdiffusion, whereas a heavy tracer approaches simple Gaussian diffusion. When particles are forced to stay in order, changing the mass of just one particle can change the character of its random motion.
Problem
Single-file diffusion describes particles constrained to a line so that they cannot pass one another. When all masses are equal, elastic collisions merely exchange velocities and the dynamics simplify greatly. That simplification disappears if one target particle has a different mass, leaving open whether mass can change the qualitative form of diffusion.
Approach
We used event-driven simulations of point particles with hard-core collisions on a periodic one-dimensional line, varying only the mass of the target particle. The light- and heavy-mass limits were then analyzed separately: repeated collisions were represented by an effective two-wall model for a light target, while a Fokker-Planck equation was derived from the Boltzmann equation for a heavy target.
What we found
A sufficiently light target exhibits non-Gaussian subdiffusion because it repeatedly bounces between neighboring particles. The simple wall model reproduces its mean-square displacement without an adjustable parameter. A heavy target instead undergoes nearly Gaussian normal diffusion, and the Fokker-Planck description agrees quantitatively with the simulations.
Why it matters
The study shows that changing the inertia of only one particle can switch the statistical character of transport even when the geometry and interactions are unchanged. It provides a tractable example of how mass, collisions, and severe confinement combine, with relevance to molecular motion in narrow pores and channels.
Keywords
single-file diffusion, particle mass, anomalous diffusion, non-Gaussian diffusion, event-driven simulation.
Paper
, “Effect of Mass on Single File Diffusion,” Nihon Reoroji Gakkaishi 52, 171–179 (2024).