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We derive and study a theoretical description for single file diffusion,i.e., diffusion in a one dimensional lattice of particles with hard coreinteraction. It is well known that for this system a tagged particle hasanomalous diffusion for long times. The novelty of the present approach is thatit allows for the derivation of correlations between a tagged particle andother particles of the system at a given distance with empty sites in between.The behavior of the correlation gives deeper insights into the processesinvolved. Numerical integration of differential equations are in good agreementwith Monte Carlo simulations.

Evolution equation for tagged particle density and correlations in single file diffusion