Fractal Dynamics in Chaotic Quantum Transport

TL;DR

This paper presents real-space quantum transport simulations in a chaotic 2D stadium cavity, revealing fractal scaling in magnetoconductance and demonstrating the effectiveness of detrended fluctuation analysis for interpreting fractality.

Contribution

It provides the first real-space, real-time quantum transport calculations for a chaotic 2D system and applies detrended fluctuation analysis to identify fractal behavior in conductance data.

Findings

Magnetoconductance exhibits fractal scaling.

Detrended fluctuation analysis effectively interprets conductance fractality.

Results qualitatively agree with previous experimental data.

Abstract

Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis -- a widely used method in time series analysis -- and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that, in turn, qualitatively agree with the previous experimental data.