Transport through cavities with tunnel barriers: a semiclassical analysis

TL;DR

This paper investigates how tunnel barriers affect quantum transport in circular cavities, using semiclassical methods to explain and predict nonmonotonic behaviors observed in numerical quantum calculations.

Contribution

It extends semiclassical approaches to include tunneling effects in ballistic transport, providing both qualitative and quantitative insights.

Findings

Semiclassical analysis matches quantum numerical results.

Nonmonotonic behavior of transmission peaks with barrier height.

Classical trajectories explain quantum transport features.

Abstract

We study the influence of a tunnel barrier on the quantum transport through a circular cavity. Our analysis in terms of classical trajectories shows that the semiclassical approaches developed for ballistic transport can be adapted to deal with the case where tunneling is present. Peaks in the Fourier transform of the energy-dependent transmission and reflection spectra exhibit a nonmonotonic behaviour as a function of the barrier height in the quantum mechanical numerical calculations. Semiclassical analysis provides a simple qualitative explanation of this behaviour, as well as a quantitative agreement with the exact calculations. The experimental relevance of the classical trajectories in mesoscopic and microwave systems is discussed.