  The dynamics of two Brownian particles trapped by two neighboring harmonic
potentials in a linear shear flow is investigated. The positional correlation
functions in this system are calculated analytically and analyzed as a function
of the shear rate and the trap distance. Shear-induced cross-correlations
between particle fluctuations along orthogonal directions in the shear plane
are found. They are linear in the shear rate, asymmetric in time, and occur for
one particle as well as between both particles. Moreover, the shear rate enters
as a quadratic correction to the well-known correlations of random
displacements along parallel spatial directions. The correlation functions
depend on the orientation of the connection vector between the potential minima
with respect to the flow direction. As a consequence, the inter-particle
cross-correlations between orthogonal fluctuations can have zero, one or two
local extrema as a function of time. Possible experiments for detecting these
predicted correlations are described.
