Time-resolved dynamics of electron wave packets in chaotic and regular quantum billiards with leads

We perform numerical studies of wave packet propagation through open quantum billiards whose classical counterparts exhibit regular and chaotic dynamics. We show that for tless than or similar totau(H)(tau(H) being the Heisenberg time), the features in the transmitted and reflected currents are directly related to specific classical trajectories connecting the billiard leads. When tgreater than or similar totau(H), the calculated quantum-mechanical current starts to deviate from its classical counterpart, with the decay rate obeying a power law that depends on the number of decay channels. In a striking contrast to the classical escape from chaotic and regular systems (exponentially fast e(-gammat) for the former versus power-law t(-xi) for the latter), the asymptotic decay of the corresponding quantum systems does not show a qualitative difference.