Fractal versus QuasiClassical Diffusive Transport in a class of quantum systems

TL;DR

This paper compares quantum transport in systems with classical chaotic versus multifractal spectra, revealing distinct transmission behaviors and fluctuation characteristics, with implications for understanding different diffusion mechanisms.

Contribution

It provides a numerical comparison of transmission properties in quantum systems with classical chaotic and multifractal spectra, highlighting fundamental differences in their diffusion and fluctuation statistics.

Findings

Inverse power law transmission dependence on sample length

Ohmic behavior only in quasi-classical diffusion cases

Distinct fluctuation statistics for fractal spectrum systems

Abstract

We compare the properties of transmission across one-dimensional finite samples which are associated with two types of "quantum diffusion", one related to a classical chaotic dynamics, the other to a multifractal energy spectrum. We numerically investigate models exhibiting one or both of these features, and we find in all cases an inverse power law dependence of the average transmission on the sample length. Although in all the considered cases the quadratic spread of wave packets increases linearly (or very close to linearly) in time for both types of dynamics, a proper Ohmic dependence is always observed only in the case of quasi-classical diffusion. The analysis of the statistics of transmission fluctuations in the case of a fractal spectrum exposes some new features, which mark further differences from ordinary diffusion, and enforce the conclusion that the two types of transmission are intrinsically different.