Quantum Chaos in Quantum Wells

TL;DR

This paper develops a semiclassical theory for resonant tunneling in quantum wells under tilted magnetic fields, linking tunneling current to periodic orbits and validating results with experiments and numerical simulations.

Contribution

It introduces a novel semiclassical approach that relates tunneling phenomena to classical orbits, including corrections from non-periodic orbits, in quantum wells.

Findings

Semiclassical approximation accurately predicts tunneling currents.

Tunneling current depends primarily on periodic orbits within the well.

Corrections from non-periodic orbits improve the theory's accuracy.

Abstract

We develop a quantitative semiclassical theory for the resosnant tunneling through a quantum well in a tilted magnetic field. It is shown, that in the leading semiclassical approximation the tunneling current depends only on periodic orbits within the quantum well. Further corrections (due to e.g. "ghost" effect) can be expressed in terms of closed, but non-periodic orbits, started at the "injection point". The results of the semiclassical theory are shown to be in good agreement with both the experimental data and numerical calculations.