  With the use of the "two-fluid model", we discuss anomalous diffusion induced
by active force dipoles in viscoelastic media. Active force dipoles, such as
proteins and bacteria, generate non-thermal fluctuating flows that lead to a
substantial increment of the diffusion. Using the partial Green's function of
the two-fluid model, we first obtain passive (thermal) two-point correlation
functions such as the displacement cross-correlation function between the two
point particles separated by a finite distance. We then calculate active
(non-thermal) one-point and two-point correlation functions due to active force
dipoles. The time correlation of a force dipole is assumed to decay
exponentially with a characteristic time scale. We show that the active
component of the displacement cross-correlation function exhibits various
crossovers from super-diffusive to sub-diffusive behaviors depending on the
characteristic time scales and the particle separation. Our theoretical results
are intimately related to the microrheology technique to detect fluctuations in
non-equilibrium environment.
