Recurrence of biased quantum walks on a line

M. Štefaňák, T. Kiss, I. Jex

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

The Pólya number of a classical random walk on a regular lattice is known to depend solely on the dimension of the lattice. For one and two dimensions it equals one, meaning unit probability of returning to the origin. This result is extremely sensitive to the directional symmetry, and any deviation from the equal probability of travelling in each direction results in a change of the character of the walk from recurrent to transient. Applying our definition of the Polya number to quantum walks on a line we show that the recurrence character of quantum walks is more stable against bias. We determine the range of parameters for which biased quantum walks remain recurrent. We find that there exist genuine biased quantum walks that are recurrent.

Original languageEnglish
Article number043027
JournalNew Journal of Physics
Volume11
DOIs
Publication statusPublished - Apr 23 2009

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random walk
deviation
symmetry

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Recurrence of biased quantum walks on a line. / Štefaňák, M.; Kiss, T.; Jex, I.

In: New Journal of Physics, Vol. 11, 043027, 23.04.2009.

Research output: Contribution to journalArticle

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