Coulomb drag in coherent mesoscopic systems

We present a theory for Coulomb drag between two mesoscopic systems. Our fo rmalism expresses the drag in terms of scattering matrices and wave functio ns, and its range of validity covers both ballistic and disordered systems. The consequences can be worked out either by analytic means, such as the r andom matrix theory, or by numerical simulations. We show that Coulomb drag is sensitive to localized states. which usual transport measurements do no t probe. For chaotic 2D systems we find a vanishing average drag, with a no nzero variance. Disordered 1D wires show a finite drag, with a large varian ce, giving rise to a possible sign change of the induced current.