  A quantitative analysis is presented for the stochastic interactions of a
pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard
spheres are hypothetically trapped by optical tweezers and allowed for random
motion near the trapped positions. The investigation focuses on the long-time
correlated Brownian motion. The mobility tensor altered by the polymer
depletion effect is computed by the boundary integral method, and the
corresponding random displacement is determined by the fluctuation-dissipation
theorem. From our computations it follows that the presence of depletion layers
around the hard spheres has a significant effect on the hydrodynamic
interactions and particle dynamics as compared to pure solvent and pure polymer
solution (no depletion) cases. The probability distribution functions of random
walks of the two interacting hard spheres that are trapped clearly shifts due
to the polymer depletion effect. The results show that the reduction of the
viscosity in the depletion layers around the spheres and the entropic force due
to the overlapping of depletion zones have a significant influence on the
correlated Brownian interactions.
