Pólya number of continuous-time quantum walks

Details Pólya number of continuous-time quantum walks Pólya number of continuous-time quantum walks

2010-04-29

arxiv.org/abs/1004.5286v2

Phys. Rev. A 81, 062319 (2010)

Physics

Quantum Physics

8 pages, no figures. Accepted for publication in Physical Review A

Scientific paper

10.1103/PhysRevA.81.062319

We propose a definition for the P\'olya 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 P\'olya 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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