Quantum transport through cantori

We study the effect of classical cantori in quantum mechanics, extending pr evious results by several groups. We find that cantori form exponential bar riers to quantum transport not only when Planck's constant exceeds the flux through the cantorus but also when it is smaller than the flux. The mechan ism of localization in the two cases is different, and we describe the swit ch from dynamical localization to a mechanism we call "retunneling'' as Pla nck's constant increases. We investigate the h dependence of the exponentia l decay for retunneling and find that the (h) over bar(-0.66) coefficient f ound previously at criticality appears to hold also away from criticality p rovided pi (h) over bar is large enough compared to the flux. Numerical evi dence as well as an analytic argument are given. Our final contribution to this subject is a phase space view of cantori in quantum mechanics. We illu strate our results using the whisker map.