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.
|Journal||Infinite Dimensional Analysis, Quantum Probability and Related Topics|
|Publication status||Published - 2013 Mar|
Bibliographical noteFunding 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