Tunneling and nonhyperbolicity in quantum dots

Due to the quantum-mechanical tunneling of the electrons through the Kolmogorov-Arnol'd-Moser (KAM) island many features in electron transport in realistic quantum dots could not be explained. A set of tunneling resonances caused by low-period stable and unstable periodic orbits led to conductance oscillations. It was found that the tunneling played a major role in mesoscopic transport. It was also found that while conductance of the small dots was dominated by the periodic oscillations, the periodic nature of oscillations became steadily obscured as the dot size increased.