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

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10.1142/S0219025713500033

Cite this

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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.",

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AU - Yoo, Hyun Jae

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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.

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KW - Interacting Fock spaces

KW - Limit distribution

KW - Quantum random walks

KW - Vacuum expectation

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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