DY 8.7: Talk
Monday, March 26, 2007, 17:45–18:00, H2
Efficiency of quantum and classical transport on graphs — •Oliver Mülken and Alexander Blumen — Theoretische Polymerphysik, Universität Freiburg, 79104 Freiburg i.Br., Germany
We propose a measure to quantify the efficiency of classical and quantum mechanical transport processes on graphs. The measure is given by the temporal decay of the space average of the probability to be still or again at the initial node of the graph, i.e., classically by p(t) and quantum mechanically by π(t), where
| (t) ≡ | | | | pj,j(t) and | | (t) ≡ | | | | πj,j(t) ≥ | | | (t)|2.
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Quantum mechanically we use the envelope env[|α(t)|2] of a lower bound obtained via the Cauchy-Schwarz inequality. Both measures only depend on the density of states (DOS). For some DOS, the measure shows a power law behavior, where the exponent for the quantum transport is twice the exponent of its classical counterpart, i.e.,
| (t)∼ t−(1+ν) and env[| | | (t)|2] ∼ t−2(1+ν).
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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.
[1] O. Mülken and A. Blumen, Phys. Rev. E 73, 066117 (2006)
