  In this work, we present an effective discrete Edwards-Wilkinson equation
aimed to describe the single-file diffusion process. The key physical
properties of the system are captured defining an effective elasticity, which
is proportional to the single particle diffusion coefficient and to the inverse
squared mean separation between particles. The effective equation gives a
description of single-file diffusion using the global roughness of the system
of particles, which presents three characteristic regimes, namely normal
diffusion, subdiffusion and saturation, separated by two crossover times. We
show how these regimes scale with the parameters of the original system.
Additional repulsive interaction terms are also considered and we analyze how
the crossover times depend on the intensity of the additional terms. Finally,
we show that the roughness distribution can be well characterized by the
Edwards-Wilkinson universal form for the different single-file diffusion
processes studied here.

Statistical Mechanics