  We study the steady state behaviour of a confined quantum Brownian particle
subjected to a space-dependent, rapidly oscillating time-periodic force. To
leading order in the period of driving, the result of the oscillating force is
an effective static potential which has a quantum dissipative contribution,
$V_{QD}$, which adds on to the classical result. This is shown using a coherent
state representation of bath oscillators. $V_{QD}$ is evaluated exactly in the
case of an Ohmic dissipation bath. It is strongest for intermediate values of
the damping, where it can have pronounced effects.
