Time operators for continuous-time and discrete-time quantum walks

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 numbe...

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Bibliographic Details
Published in:arXiv.org 2020-06
Main Authors: Funakawa, Daiju, Matsuzawa, Yasumichi, Suzuki, Akito, Sasaki, Itaru, Teranishi, Noriaki
Format: Article
Language:English
Subjects:
Commutation
Concrete construction
Military deployment
Offshore
Operators
Online Access:Get full text
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Summary: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.
ISSN:2331-8422