Transport properties of continuous-time quantum walks on Sierpinski fractals

Zoltán Darázs, Anastasiia Anishchenko, Tamás Kiss, Alexander Blumen, Oliver Mülken

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14 Citations (Scopus)

Abstract

We model quantum transport, described by continuous-time quantum walks (CTQWs), 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.

Original languageEnglish
Article number032113
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume90
Issue number3
DOIs
Publication statusPublished - Sep 12 2014

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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