Interacting fock spaces and the moments of the limit distributions for quantum random walks

Chul Ki Ko; Hyun Jae Yoo

doi:10.1142/S0219025713500033

Interacting fock spaces and the moments of the limit distributions for quantum random walks

Chul Ki Ko, Hyun Jae Yoo

University College

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We investigate the limit distributions of the discrete time quantum random walks on lattice spaces via a spectral analysis of concretely given self-adjoint operators. We discuss the interacting Fock spaces associated with the limit distributions. Thereby, we represent the moments of the limit distribution by vacuum expectation of the monomials of the Fock operator. We get formulas not only for one-dimensional walks but also for high-dimensional walks.

Original language	English
Article number	1350003
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	16
Issue number	1
DOIs	https://doi.org/10.1142/S0219025713500033
Publication status	Published - 2013 Mar

Bibliographical note

Funding Information:
We are grateful to Boyoon Seo for numerical computations. H. J. Yoo would like to thank David Brydges for warm hospitality and giving many comments on this study. Many supports and hospitality from PIMS during his visit to UBC is greatly appreciated. H. J. Yoo was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-013-C00007).

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Mathematical Physics
Applied Mathematics

Access to Document

10.1142/S0219025713500033

Cite this

@article{e0632f18f7b943b5b062e03812533997,

title = "Interacting fock spaces and the moments of the limit distributions for quantum random walks",

abstract = "We investigate the limit distributions of the discrete time quantum random walks on lattice spaces via a spectral analysis of concretely given self-adjoint operators. We discuss the interacting Fock spaces associated with the limit distributions. Thereby, we represent the moments of the limit distribution by vacuum expectation of the monomials of the Fock operator. We get formulas not only for one-dimensional walks but also for high-dimensional walks.",

author = "Ko, {Chul Ki} and Yoo, {Hyun Jae}",

note = "Funding Information: We are grateful to Boyoon Seo for numerical computations. H. J. Yoo would like to thank David Brydges for warm hospitality and giving many comments on this study. Many supports and hospitality from PIMS during his visit to UBC is greatly appreciated. H. J. Yoo was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-013-C00007).",

year = "2013",

month = mar,

doi = "10.1142/S0219025713500033",

language = "English",

volume = "16",

journal = "Infinite Dimensional Analysis, Quantum Probability and Related Topics",

issn = "0219-0257",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "1",

}

TY - JOUR

T1 - Interacting fock spaces and the moments of the limit distributions for quantum random walks

AU - Ko, Chul Ki

AU - Yoo, Hyun Jae

N1 - Funding Information: We are grateful to Boyoon Seo for numerical computations. H. J. Yoo would like to thank David Brydges for warm hospitality and giving many comments on this study. Many supports and hospitality from PIMS during his visit to UBC is greatly appreciated. H. J. Yoo was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-013-C00007).

PY - 2013/3

Y1 - 2013/3

N2 - We investigate the limit distributions of the discrete time quantum random walks on lattice spaces via a spectral analysis of concretely given self-adjoint operators. We discuss the interacting Fock spaces associated with the limit distributions. Thereby, we represent the moments of the limit distribution by vacuum expectation of the monomials of the Fock operator. We get formulas not only for one-dimensional walks but also for high-dimensional walks.

AB - We investigate the limit distributions of the discrete time quantum random walks on lattice spaces via a spectral analysis of concretely given self-adjoint operators. We discuss the interacting Fock spaces associated with the limit distributions. Thereby, we represent the moments of the limit distribution by vacuum expectation of the monomials of the Fock operator. We get formulas not only for one-dimensional walks but also for high-dimensional walks.

UR - http://www.scopus.com/inward/record.url?scp=84878697793&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878697793&partnerID=8YFLogxK

U2 - 10.1142/S0219025713500033

DO - 10.1142/S0219025713500033

M3 - Article

AN - SCOPUS:84878697793

SN - 0219-0257

VL - 16

JO - Infinite Dimensional Analysis, Quantum Probability and Related Topics

JF - Infinite Dimensional Analysis, Quantum Probability and Related Topics

IS - 1

M1 - 1350003

ER -

Interacting fock spaces and the moments of the limit distributions for quantum random walks

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this