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Slow transport by continuous time quantum walks

Oliver Muelken·Alexander Blumen
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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.

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Oliver Muelken, Alexander Blumen. 2004-10-29. Slow transport by continuous time quantum walks. https://doi.org/10.1103/physreve.71.016101

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