  The quantum ratchet effect in fully chaotic systems is approached by
studying, for the first time, \emph{statistical} properties of the ratchet
current over well-defined sets of initial states. Natural initial states in a
semiclassical regime are those that are \emph{phase-space uniform} with the
\emph{maximal possible} resolution of one Planck cell. General arguments in
this regime, for quantum-resonance values of a scaled Planck constant $\hbar$,
predict that the distribution of the current over all such states is a
zero-mean Gaussian with variance $\sim D\hbar^{2}/(2\pi^{2})$, where $D$ is the
chaotic-diffusion coefficient. This prediction is well supported by extensive
numerical evidence. The average strength of the effect, measured by the
variance above, is \emph{significantly larger} than that for the usual momentum
states and other states. Such strong effects should be experimentally
observable.
