Correlation of Two Coupled Particles in Viscoelastic Medium

Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find thatviscoelastic relaxation plays a significant role in modifying thecorrelation, particularly the cross correlation. We also find thatboth the real and imaginary parts of the response function aresignificantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the crosscorrelation response function exhibits a net energy loss (gain)behavior when the elasticity parameter of the medium is larger(smaller) than the critical value for Kelvin (Maxwell)viscoelastic fluid. Some implication of our results and theirconnection with previous works are discussed.