Langevin formulation for single-file diffusion

We introduce a stochastic equation for the microscopic motion of a tagged particle in the single-file model. This equation provides a compact representation of several of the system's properties such as fluctuation-dissipation and linear-response relations, achieved by means of a diffusion noise approach. Most importantly, the proposed Langevin equation reproduces quantitatively the three temporal regimes and the corresponding time scales: ballistic, diffusive, and subdiffusive.