The quantum ratchet effect in fully chaotic systems is approached by studying, for the first time, statistical properties of the ratchet current over well-defined sets of initial states. Natural initial states in a semiclassical regime are those that are phase-space uniform with the maximal possible resolution of one Planck cell. General arguments in this regime predict that the distribution of the current over all such states is a zero-mean Gaussian with variance ≈ D\hbar²/(2π²), where D is the chaotic-diffusion coefficient and \hbar is a scaled Planck constant. This prediction is well confirmed by numerical results.<br>
Similar distributions, with a variance generally smaller than the above one, are exhibited by the momentum states and by approximations of the maximally uniform states. All these states and the model systems considered should be experimentally realizable.