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

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.

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