Tagged-Particle Statistics in Single-File Motion with Random-Acceleration and Langevin Dynamics.

In the simplest model of single-file diffusion, N point particles wander on a segment of the x axis of length L, with hard core interactions, which prevent passing, and with overdamped Brownian dynamics λ x ˙ = η (t) , where η (t) has the form of Gaussian white noise with zero mean. In 1965 Harris showed that in the limit N → ∞ , L → ∞ with constant ρ = N / L , the mean square displacement of a tagged particle grows subdiffusively, as t 1 / 2 , for long times. Recently, it has been shown that the proportionality constants of the t 1 / 2 law for randomly-distributed initial positions of the particles and for equally-spaced initial positions are not the same, but have ratio 2 . In this paper we consider point particles on the x axis, which collide elastically, and which move according to (i) random-acceleration dynamics x ¨ = η (t) and (ii) Langevin dynamics x ¨ + λ x ˙ = η (t) . The mean square displacement and mean-square velocity of a tagged particle are analyzed for both types of dynamics and for random and equally-spaced initial positions and Gaussian-distributed initial velocities. We also study tagged particle statistics, for both types of dynamics, in the spreading of a compact cluster of particles, with all of the particles initially at the origin. [ABSTRACT FROM AUTHOR]