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

TL;DR

This study numerically investigates wave packet dynamics in open quantum billiards with regular and chaotic classical counterparts, revealing short-time classical trajectory influences and long-time quantum decay behaviors independent of classical chaos.

Contribution

It demonstrates the distinct short-time classical trajectory effects and the universal power-law decay in long-time quantum dynamics regardless of classical chaos or regularity.

Findings

Short-time wave features relate to classical trajectories

Long-time decay follows a power law independent of classical dynamics

Quantum decay depends on the number of channels

Abstract

We perform numerical studies of the wave packet propagation through open quantum billiards whose classical counterparts exhibit regular and chaotic dynamics. We show that for t less or similar to tau (tau being the Heisenberg time), the features in the transmitted and reflected currents are directly related to specific classical trajectories connecting the billiard leads. In contrast, the long-time asymptotics of the wave packet dynamics is qualitatively different for classical and quantum billiards. In particularly, the decay of the quantum system obeys a power law that depends on the number of decay channels, and is not sensitive to the nature of classical dynamics (chaotic or regular).