Efficiency of quantum and classical transport on graphs
arXiv:quant-ph/0602120 · doi:10.1103/PhysRevE.73.066117
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
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- Dark states of quantum search cause imperfect detection
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- The spectral dimension controls the decay of the quantum first detection probability
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- Quantum scattering model of energy transfer in photosynthetic complexes
- Perturbed graphs achieve unit transport efficiency without environmental noise
- Continuous-Time Quantum Walk on Penrose Lattice