Coherent transport on Apollonian networks and continuous-time quantum walks
arXiv:0810.0824 · doi:10.1103/PhysRevE.78.052103
Abstract
We study the coherent exciton transport on Apollonian networks generated by simple iterative rules. The coherent exciton dynamics is modeled by continuous-time quantum walks and we calculate the transition probabilities between two nodes of the networks. We find that the transport depends on the initial nodes of the excitation. For networks less than the second generation the coherent transport shows perfect revivals when the initial excitation starts at the central node. For networks of higher generation, the transport only shows partial revivals. Moreover, we find that the excitation is most likely to be found at the initial nodes while the coherent transport to other nodes has a very low probability. In the long time limit, the transition probabilities show characteristic patterns with identical values of limiting probabilities. Finally, the dynamics of quantum transport are compared with the classical transport modeled by continuous-time random walks.
5 pages, 6 figues. Submitted to Phys. ReV. E
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- Deterministic weighted scale-free small-world networks
- Generalized open quantum walks on Apollonian networks
- Transport efficiency of continuous-time quantum walks on graphs
- Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder
- Scattering and transport properties of tight-binding random networks
- Pseudo-Hermitian continuous-time quantum walks
- How the site degree influences quantum probability on inhomogeneous substrates
- Binary Apollonian networks
- The extended star graph as a light-harvesting-complex prototype: excitonic absorption speedup by peripheral energy defect tuning
- Random Apollonian networks with tailored clustering coefficient
- Characterizing several properties of high-dimensional random Apollonian networks
- Perturbed graphs achieve unit transport efficiency without environmental noise