The dynamics of hard-core interacting Brownian particles in an external potential field is studied in one dimension. Using the Jepsen line we find a very general and simple formula relating the motion of the tagged center particle, with the classical, time dependent single particle reflection R and transmission T coefficients. Our formula describes rich physical behaviors both in equilibrium and the approach to equilibrium of this many body problem.
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Barkai et al. (2009) studied this question.
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