### 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 language | English |
---|---|

Article number | 043027 |

Journal | New Journal of Physics |

Volume | 11 |

DOIs | |

Publication status | Published - Apr 23 2009 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*New Journal of Physics*,

*11*, [043027]. https://doi.org/10.1088/1367-2630/11/4/043027

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

Research output: Contribution to journal › Article

*New Journal of Physics*, vol. 11, 043027. https://doi.org/10.1088/1367-2630/11/4/043027

}

TY - JOUR

T1 - Recurrence of biased quantum walks on a line

AU - Štefaňák, M.

AU - Kiss, T.

AU - Jex, I.

PY - 2009/4/23

Y1 - 2009/4/23

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=66249089039&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=66249089039&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/11/4/043027

DO - 10.1088/1367-2630/11/4/043027

M3 - Article

AN - SCOPUS:66249089039

VL - 11

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 043027

ER -