Conditional limit measure of a one-dimensional quantum walk with an absorbing sink

Mohamed Sabri, Etsuo Segawa, Martin Štefaňák

研究成果: Article査読

抄録

We consider a two-state quantum walk on a line where after the first step an absorbing sink is placed at the origin. The probability of finding the walker at position j, conditioned on that it has not returned to the origin, is investigated in the asymptotic limit. We prove a limit theorem for the conditional probability distribution and show that it is given by the Konno's density function modified by a prefactor ensuring that the distribution vanishes at the origin. In addition, we discuss the relation to the problem of recurrence of a quantum walk and determine the Pólya number. Our approach is based on path counting and the stationary phase approximation.

本文言語English
論文番号012136
ジャーナルPhysical Review A
98
1
DOI
出版ステータスPublished - 2018 7 27

ASJC Scopus subject areas

  • 原子分子物理学および光学

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