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.
arXiv comment10 pages, 6 figures
References in corpus (26)
- Statistical mechanics of complex networks
- Photonic Floquet Topological Insulators
- Structural Vulnerability of the North American Power Grid
- Quantum Computation and Decision Trees
- Quantum walks: a comprehensive review
- First-passage times in complex scale-invariant media
- A 2D Quantum Walk Simulation of Two-Particle Dynamics
- Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks
- Recurrence for discrete time unitary evolutions
- Recurrence and Pólya number of quantum walks
- Survival Probabilities in Coherent Exciton Transfer with Trapping
- Coherent exciton transport in dendrimers and continuous-time quantum walks
- Quantum walk approach to search on fractal structures
- 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
- Search on a Fractal Lattice using a Quantum Random Walk
- Recurrences in three-state quantum walks on a plane
- Full-revivals in 2-D Quantum Walks
- Pólya number of continuous-time quantum walks
- Transport efficiency in topologically disordered networks with environmentally induced diffusion
- Harmonic functions and the spectrum of the Laplacian on the Sierpinski carpet
- Slow Excitation Trapping in Quantum Transport with Long-Range Interactions
- Geometrical aspects of quantum walks on random two-dimensional structures
- Recurrence and Polya number of general one-dimensional random walks
Cited by in corpus (18)
- Experimental Two-dimensional Quantum Walk on a Photonic Chip
- Experimental Quantum Fast Hitting on Hexagonal Graphs
- Non-Markovian continuous-time quantum walks on lattices with dynamical noise
- Complex Quantum Networks: a Topical Review
- Noisy quantum walks of two indistinguishable interacting particles
- Scaling relations in the diffusive infiltration in fractals
- Transport efficiency of continuous-time quantum walks on graphs
- Colloquium: Synthetic quantum matter in non-standard geometries
- Percolation assisted excitation transport in discrete-time quantum walks
- Swift chiral quantum walks
- Anomalous quantum transport in fractal lattices
- Quantum walks with spatiotemporal fractal disorder
- Coherent transport over an explosive percolation lattice
- Bose-Einstein condensation in exotic lattice geometries
- Shining Light on Quantum Transport in Fractal Networks
- Universal scaling hypothesis of quantum spatial search in complex networks
- Continuous-Time Quantum Walk on Penrose Lattice
- Perturbed graphs achieve unit transport efficiency without environmental noise