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  • O Polyaovském čísle klasické namátkové procházky na pravidelné mřížce je známo, že závisí pouze na dimenzi mřížky. Pro jeden a dva rozměry se rovná jedné, tj. pravděpodobnost návratu k počátku je jedna. Tento výsledek je velmi citlivý na směrovou symetrii, a jakékoliv odchylky od stejné pravděpodobnosti cestování v každém směru vede ke změně charakteru této chůze od opakující se přechodné. Ukázali jsme, že při uplatnění naší definice Polyaova čísla kvantové procházky, je rekurence kvantové procházky stabilnější proti podjatosti (cs)
  • 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 Pólya 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.
  • 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 Pólya 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. (en)
Title
  • Recurrence of Biased Quantum Walks on a Line
  • Recurrence of Biased Quantum Walks on a Line (en)
  • Rekurence nevyvážených kvantových procházek na přímce (cs)
skos:prefLabel
  • Recurrence of Biased Quantum Walks on a Line
  • Recurrence of Biased Quantum Walks on a Line (en)
  • Rekurence nevyvážených kvantových procházek na přímce (cs)
skos:notation
  • RIV/68407700:21340/09:04155125!RIV09-MSM-21340___
http://linked.open...avai/riv/aktivita
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  • P(LC06002), Z(MSM6840770039)
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  • 0
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  • 338407
http://linked.open...ai/riv/idVysledku
  • RIV/68407700:21340/09:04155125
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  • quantum walk; recurrence (en)
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  • GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV
  • [34CDD789387B]
http://linked.open...i/riv/nazevZdroje
  • New Journal of Physics
http://linked.open...in/vavai/riv/obor
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  • 11
http://linked.open...iv/tvurceVysledku
  • Jex, Igor
  • Kiss, T.
  • Štefaňák, Martin
http://linked.open...ain/vavai/riv/wos
  • 000265678400027
http://linked.open...n/vavai/riv/zamer
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  • 1367-2630
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  • 21340
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