Statistical approach to quantum chaotic ratchets.
The quantum ratchet effect in fully chaotic systems is approached by studying 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 variant Planck's over 2pi , predict that the distribution of the current over all such states is a zero-mean Gaussian with variance approximately Dvariant Planck's over 2pi2/(2pi2) , 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.
Dana
Itzhack
I
Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.