Effect of Mass on Single File Diffusion

Particles on a one-dimensional line exhibit so-called single-file diffusion, which has been investigated as a simple model of diffusion. In single-file diffusion, a constituent particle interacts only with the two neighboring particles, and the order of the particles remains unchanged. This strong constraint makes the analyses of the single particle diffusion to be tractable. When all the particles have the same mass, the dynamics can be largely simplified; the trajectories of particles appear as if they are intersecting with each other. We consider the general cases where the mass of a target particle is different from that of the other particles, and the simple situation mentioned above no longer holds. In this study, we numerically investigate the dynamics of a single target particle with various masses. When the target particle is heavy, the target particle almost shows simple Gaussian diffusion. In contrast, the target particle exhibits anomalous non-Gaussian diffusion when the target particle is sufficiently light. We also perform theoretical analyses to reproduce the mean square displacements in large and small mass cases.