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We study the Single File Diffusion (SFD) of a cyclic chain of particles thatcannot cross each other, in a thermal bath, with long ranged interactions, andarbitrary damping. We present simulations that exhibit new behaviorsspecifically associated to systems of small number of particles and to smalldamping. In order to understand those results, we present an original analysisbased on the decomposition of the particles motion in the normal modes of thechain. Our model explains all dynamic regimes observed in our simulations, andprovides convincing estimates of the crossover times between those regimes.

Single File Diffusion of particles with long ranged interactions: damping and finite size effects