Slow transport by continuous time quantum walks

Abstract

Continuous time quantum walks (CTQW) do not necessarily perform better than their classical counterparts, the continuous time random walks (CTRW). For one special graph, where a recent analysis showed that in a particular direction of propagation the penetration of the graph is faster by CTQWs than by CTRWs, we demonstrate that in another direction of propagation the opposite is true; In this case a CTQW initially localized at one site displays a slow transport. We furthermore show that when the CTQW's initial condition is a totally symmetric superposition of states of equivalent sites, the transport gets to be much more rapid.

5 pages, 7 figures, accepted for publication in Phys. Rev. E

References in corpus (6)

• Statistical mechanics of complex networks
• Evolution of networks
• Quantum random walks - an introductory overview
• Quantum Computation and Decision Trees
• An example of the difference between quantum and classical random walks
• Thermodynamic formalism for field driven Lorentz gases

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