Transport properties of continuous-time quantum walks on Sierpinski fractals
arXiv:1405.5078 · doi:10.1103/PhysRevE.90.032113
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.
10 pages, 6 figures
References in corpus (11)
- First-passage times in complex scale-invariant media
- A 2D Quantum Walk Simulation of Two-Particle Dynamics
- Survival Probabilities in Coherent Exciton Transfer with Trapping
- Coherent exciton transport in dendrimers and continuous-time quantum walks
- Efficiency of quantum and classical transport on graphs
- Dynamics of continuous-time quantum walks in restricted geometries
- Recurrence of biased quantum walks on a line
- Survival probability in a one-dimensional quantum walk on a trapped lattice
- Recurrences in three-state quantum walks on a plane
- Full-revivals in 2-D Quantum Walks
- Slow Excitation Trapping in Quantum Transport with Long-Range Interactions
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- Shining Light on Quantum Transport in Fractal Networks
- Coherent transport over an explosive percolation lattice
- Perturbed graphs achieve unit transport efficiency without environmental noise
- Universal scaling hypothesis of quantum spatial search in complex networks
- Continuous-Time Quantum Walk on Penrose Lattice