  We investigate the single-file dynamics of a tagged particle in a system
consisting of N hardcore interacting particles (the particles cannot pass each
other) which are diffusing in a one-dimensional system where the particles have
different diffusion constants. For the two particle case an exact result for
the conditional probability density function (PDF) is obtained for arbitrary
initial particle positions and all times. The two-particle PDF is used to
obtain the tagged particle PDF. For the general N-particle case (N large) we
perform stochastic simulations using our new computationally efficient
stochastic simulation technique based on the Gillespie algorithm. We find that
the mean square displacement for a tagged particle scales as the square root of
time (as for identical particles) for long times, with a prefactor which
depends on the diffusion constants for the particles; these results are in
excellent agreement with very recent analytic predictions in the mathematics
literature.

Statistical Mechanics;Soft Condensed Matter