Periodic Orbit Theory of the Transition to Chaos in Quantum Wells

TL;DR

This paper develops an analytic periodic orbit theory to explain the oscillations in the density of states in tilted magnetic quantum wells, revealing how chaos influences experimental observations.

Contribution

It introduces a novel analytic framework linking periodic orbits and chaos to density of states oscillations in quantum wells under tilted magnetic fields.

Findings

Main oscillations originate from simple periodic orbits.

Identifies sequence of destabilizations and restabilizations with increasing chaos.

Explains re-entrant frequency-doubling observed in experiments.

Abstract

An analytic theory is developed for the density of states oscillations in quantum wells in a magnetic field which is tilted with respect to the barrier planes. The main oscillations are found to come from the simplest one or two-bounce periodic orbits. We calculate their period and stability analytically and find an infinite sequence of destabilizations followed by restabilizations as the chaos parameter increases. This phenomenon explains the re-entrant frequency-doubling of the density of states peaks observed in recent magnetotunneling experiments.