Transport properties of continuous-time quantum walks on Sierpinski fractals

Darázs, Zoltán and Anishchenko, A. and Kiss, Tamás and Blumen, A. and Mülken, O. (2014) Transport properties of continuous-time quantum walks on Sierpinski fractals. PHYSICAL REVIEW E - STATISTICAL, NONLINEAR AND SOFT MATTER PHYSICS (2001-2015), 90 (3). ISSN 1539-3755

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Abstract

We model quantum transport, described by continuous-time quantum walks (CTQW), on deterministic Sier- pinski 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 localiza- tion, 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.

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