Statistical Approach to Quantum Chaotic Ratchets

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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, for quantum-resonance values of a scaled Planck constant ℏ, predict that the distribution of the current over all such states is a zero-mean Gaussian with variance Dℏ²/(2π²), 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 significantly larger than that for the usual momentum states and other states. Such strong effects should be experimentally observable.