CTM/Zeta Correspondence

In our previous work, we investigated the relation between zeta functions and discrete-time models including random and quantum walks. In this paper, we introduce a zeta function for the continuous-time model (CTM) and consider CTMs including the corresponding random and quantum walks on the d-dimensional torus.
Comment: 9 pages, minor corrections, Quantum Studies: Mathematics and Foundations, Volume 9, pp.165-173 (2022)