Quantum transport on small-world networks: A continuous-time quantum walk approach
arXiv:0705.1608 · doi:10.1103/PhysRevE.76.051125
Abstract
We consider the quantum mechanical transport of (coherent) excitons on small-world networks (SWN). The SWN are build from a one-dimensional ring of N nodes by randomly introducing B additional bonds between them. The exciton dynamics is modeled by continuous-time quantum walks and we evaluate numerically the ensemble averaged transition probability to reach any node of the network from the initially excited one. For sufficiently large B we find that the quantum mechanical transport through the SWN is, first, very fast, given that the limiting value of the transition probability is reached very quickly; second, that the transport does not lead to equipartition, given that on average the exciton is most likely to be found at the initial node.
8 pages, 8 figures (high quality figures available upon request)
References in corpus (23)
- Statistical mechanics of complex networks
- Evolution of networks
- Quantum Computation and Decision Trees
- Statistics of energy levels and eigenfunctions in disordered systems
- Spectra of "Real-World" Graphs: Beyond the Semi-Circle Law
- An example of the difference between quantum and classical random walks
- Diffusion, localization and dispersion relations on ``small-world'' lattices
- Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs
- Chaotic Scattering on Graphs
- Coherent exciton transport in dendrimers and continuous-time quantum walks
- Small-World Networks: Links with long-tailed distributions
- Universality in Complex Networks: Random Matrix Analysis
- Relaxation Properties of Small-World Networks
- Periodic-Orbit Theory of Anderson Localization on Graphs
- Spacetime structures of continuous time quantum walks
- Efficiency of quantum and classical transport on graphs
- Scars on quantum networks ignore the Lyapunov exponent
- Quantum computing of delocalization in small-world networks
- Localization-Delocalization Transition of Electron States in a Disordered Quantum Small World Network
- Asymmetries in symmetric quantum walks on two-dimensional networks
- Coherent dynamics on hierarchical systems
- Quantum and classical diffusion in small-world networks
- Modeling Disordered Quantum Systems with Dynamical Networks
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- Multifractal analysis of eigenvectors of smallworld networks
- Quantum transport efficiency in noisy random-removal and small-world networks
- The Heun differential equation and the Gauss differential equation related to quantum walks
- Quantum Search Algorithms on Hierarchical Networks
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- Coherent transport over an explosive percolation lattice
- Clustering-induced localization of quantum walks on networks
- Decoherence and classicalization of continuous-time quantum walks on graphs
- Exact simulation of coined quantum walks with the continuous-time model
- Enhancing the spreading of quantum walks on star graphs by additional bonds
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- Perturbed graphs achieve unit transport efficiency without environmental noise
- Temporal nonclassicality in continuous-time quantum walks
- Directionality and quantum backfire in continuous-time quantum walks from delocalized states: Exact results
- Fluctuations and Persistence in Quantum Diffusion on Regular Lattices
- Small-World Disordered Lattices: Spectral Gaps and Diffusive Transport
- Time Reversibility of Quantum Diffusion in Small-world Networks
- A simple model of Small-World Quantum Networks