Single-file diffusion refers to the motion particles in unidimensional systems. Since the particles cannot pass each other their order is maintained. This fact leads to strong deviation from normal diffusion, e.g the mean-square-displacement (MSD) of tagged particle is ~ t^1/2 instead of linear dependence on time for normal diffusion.

In my talk, I will present two methods for solving this many-body problem, I shall discuss the effect of two initial conditions on the behavior of the tagged particle: uniform distribution of the particles and equally spaced particles (particles initially on a lattice). The effect is shown by the differences of MSD and correlation function for the two initial conditions. Later I will discuss the violation of Einstein relation, and its dependence on the initial condition.

Our work shows that initial conditions determine the long time limit of the dynamics, and in this sense the system never forgets its initial state in complete contrast with thermal system (i.e closed system which attains equilibrium independent of the initial state).