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 -