# The Hamiltonians Generating One-Dimensional Discrete-Time Quantum Walks

@article{Tate2013TheHG, title={The Hamiltonians Generating One-Dimensional Discrete-Time Quantum Walks}, author={T. Tate}, journal={Interdisciplinary Information Sciences}, year={2013}, volume={19}, pages={149-156} }

An explicit formula of the Hamiltonians generating one-dimensional discrete-time quantum walks is given. The formula is deduced by using the algebraic structure introduced previously. The square of the Hamiltonian turns out to be an operator without, essentially, the `coin register', and hence it can be compared with the one-dimensional continuous-time quantum walk. It is shown that, under a limit with respect to a parameter, which expresses the magnitude of the diagonal components of the… Expand

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We study the spectral analysis and the scattering theory for time evolution operators of position-dependent quantum walks. Our main purpose of this paper is construction of generalized eigenfunctions… Expand

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