  We develop a theoretical framework to study the effective dynamics of a
tracer immersed in a nonequilibrium bath consisting of active particles. By
using a mean-field approximation and extending the linearized Dean equation to
nonequilibrium environment, we derive a generalized Langevin equation for the
tracer particle, wherein colored noise terms and a memory kernel reflect the
roles of interactions between tracer and bath particles as well as activity of
the bath. In particular, we obtain a self-consistent equation to calculate the
long time diffusion coefficient and mobility of tracer, finding that they both
increase non-linearly with bath activity, in good consistents with direct
simulation results.
