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arXiv · 1004.5286

Pólya number of continuous-time quantum walks

Z. Darázs·T. Kiss
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Abstract

We propose a definition for the Pólya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in order to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, higher dimensional integer lattices and a number of other graphs and calculate their Pólya number. For the timing of the measurements a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.

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Z. Darázs, T. Kiss. 2010-05-19. Pólya number of continuous-time quantum walks. https://doi.org/10.1103/physreva.81.062319

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