Transport properties of continuous-time quantum walks on Sierpinski fractals

TL;DR

This paper investigates quantum transport via continuous-time quantum walks on Sierpinski fractals, revealing localization phenomena and showing that spectral dimension alone does not fully predict quantum walk behavior.

Contribution

It provides a detailed analysis of quantum transport on Sierpinski gaskets and carpets, highlighting differences from classical random walks and the limitations of spectral dimension as a predictor.

Findings

Localization occurs in Sierpinski gaskets for small networks

Transport trends towards localization in larger carpets

Spectral dimension does not fully determine quantum walk evolution

Abstract

We model quantum transport, described by continuous-time quantum walks (CTQW), on deterministic Sierpinski fractals, differentiating between Sierpinski gaskets and Sierpinski carpets, along with their dual structures. The transport efficiencies are defined in terms of the exact and the average return probabilities, as well as by the mean survival probability when absorbing traps are present. In the case of gaskets, localization can be identified already for small networks (generations). For carpets, our numerical results indicate a trend towards localization, but only for relatively large structures. The comparison of gaskets and carpets further implies that, distinct from the corresponding classical continuous-time random walk, the spectral dimension does not fully determine the evolution of the CTQW.