Efficiency of quantum and classical transport on graphs

Abstract

We propose a measure to quantify the efficiency of classical and quantum mechanical transport processes on graphs. The measure only depends on the density of states (DOS), which contains all the necessary information about the graph. For some given (continuous) DOS, the measure shows a power law behavior, where the exponent for the quantum transport is twice the exponent of its classical counterpart. For small-world networks, however, the measure shows rather a stretched exponential law but still the quantum transport outperforms the classical one. Some finite tree-graphs have a few highly degenerate eigenvalues, such that, on the other hand, on them the classical transport may be more efficient than the quantum one.

5 pages, 3 figures

References in corpus (2)

• Coherent exciton transport in dendrimers and continuous-time quantum walks
• Quantum and classical diffusion in small-world networks

Cited by in corpus (8)

• Survival Probabilities in Coherent Exciton Transfer with Trapping
• Quantum transport on small-world networks: A continuous-time quantum walk approach
• Exact analytical results for quantum walks on star graph
• Dynamics of continuous-time quantum walks in restricted geometries
• Continuous-time quantum walks on one-dimension regular networks
• Coherent exciton transport and trapping on long-range interacting cycles
• Universal Behavior of Quantum Walks with Long-Range Steps
• Diffusion on a heptagonal lattice