Time operators for continuous-time and discrete-time quantum walks
Mathematical Physics
2020-06-23 v3 math.MP
Spectral Theory
Abstract
We construct concrete examples of time operators for both continuous and discrete-time homogeneous quantum walks, and we determine their deficiency indices and spectra. For a discrete-time quantum walk, the time operator can be self-adjoint if the time evolution operator has a non-zero winding number. In this case, its spectrum becomes a discrete set of real numbers.
Cite
@article{arxiv.1901.10665,
title = {Time operators for continuous-time and discrete-time quantum walks},
author = {Daiju Funakawa and Yasumichi Matsuzawa and Akito Suzuki and Itaru Sasaki and Noriaki Teranishi},
journal= {arXiv preprint arXiv:1901.10665},
year = {2020}
}
Comments
This is a pre-print of an article published in Letters in Mathematical Physics. The final authenticated version is available online at: https://doi.org/10.1007/s11005-020-01299-5