TY - JOUR

T1 - Conditional limit measure of a one-dimensional quantum walk with an absorbing sink

AU - Sabri, Mohamed

AU - Segawa, Etsuo

AU - Štefaňák, Martin

N1 - Funding Information:
E.S. acknowledges financial supports from the Grant-in-Aid for Young Scientists (B) and of Scientific Research (B) of the Japan Society for the Promotion of Science (Grants No. 16K17637 and No. 16K03939). M.Š. is grateful for financial support from GAČR under Grant No. 17-00844S and from MŠMT under Grant No. RVO 14000.
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/7/27

Y1 - 2018/7/27

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.98.012136

DO - 10.1103/PhysRevA.98.012136

M3 - Article

AN - SCOPUS:85051229609

VL - 98

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 1

M1 - 012136

ER -