Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 52, Issue 39, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/ab370b
Keywords
quantum walk; dynamical system; scattering
Categories
Funding
- Japan Society for the Promotion of Science [25400208, 18K03401, 15H02055, 19K03616]
- Research Origin for Dressed Photon
- Grants-in-Aid for Scientific Research [19K03616, 15H02055, 18K03401] Funding Source: KAKEN
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We consider the Grover walk model on a connected finite graph with two infinite length tails and we set an l(infinity)-infinite external source from one of the tails as the initial state. We show that for any connected internal graph, a stationary state exists, moreover a perfect transmission to the opposite tail always occurs in the long time limit. We also show that the lower bound of the norm of the stationary measure restricted to the internal graph is proportional to the number of edges of this graph. Furthermore when we add more tails (e.g. r-tails) to the internal graph, then we find that from the temporal and spatial global view point, the scattering to each tail in the long time limit coincides with the local one-step scattering manner of the Grover walk at a vertex whose degree is (r + 1).
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