Two harmonically coupled Brownian particles in random media

We study the behaviour of two Brownian particles coupled by an elastic harm onic force in a quenched disordered medium. We found that to first order in disorder strength, the relative motion weakens ( with respect to the refer ence state of a Brownian particle with the double mass) the effect of the q uenched forces on the centre-of-mass motion of the Brownian particles, so t hat the motion will become less subdiffusive (superdiffusive) for potential ( solenoidal) disorder. The mean-square relative distance between the part icles behaves in a different way depending on whether the particles are fre e to move or one particle is anchored in the space. While the effect of non potential disorder consists in increasing the mean-square distance in both cases, the potential disorder decreases the mean-square distance, when the particles are free to move, and increases it when one particle is anchored in the space.