# Propagation and spectral properties of quantum walks in electric fields

@inproceedings{Cedzich2013PropagationAS, title={Propagation and spectral properties of quantum walks in electric fields}, author={Christopher Cedzich and T. Ryb'ar and Albert H. Werner and Andrea Alberti and Maximilian Genske and Reinhard F. Werner}, year={2013} }

We study one-dimensional quantum walks in a homogenous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field Φ, e.g., on whether Φ/(2π) is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given…

## 11 Citations

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It is found that the dynamics of the walker probability distribution and the corresponding standard deviation, the coin-walker entanglement, and the quantum-to-classical transition of the discrete-time quantum walk model can be approximately generated by the optimized time-independent Hamiltonian.

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An overview of quantum cellular automata theory is given, with particular focus on structure results; computability and universality results; and quantum simulation results.

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In the one-dimensional cases, these results are extended to general two-state quantum walks and three-state Grover walks, while providing a partial calculation for absorption in d-dimensional Grover walk by a d-1-dimensional wall.

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