# Single File Dynamics

The basic single file process is the diffusion of N (N → ∞) identical Brownian hard spheres in a quasi-one-dimensional channel of length L (L → ∞), such that the spheres do not jump one on top of the other, and the average particle's density is approximately fixed. The most known statistical properties in this process are that the mean square displacement (MSD) of a particle in the file follows, MSD~t1/2 and its probability density function (PDF) is a Gaussian in position with a variance, MSD.

I’LL focus in the talk on three new variants in file dynamics and address the following questions:

(*) First, the question about the origin of the unique scaling, MSD~t1/2, in simple files, is addressed using scaling law analysis and a new approach for full mathematical computations in normal files.

(*) The MSD is derived in normal files with particles’ density that is not fixed and with particles that are not identical, yet, the diffusion coefficients of the particles are distributed according to a probability density function.

(*) Files with anomalous basic dynamics, both renewal ones and those that are not renewal are solved.