Propagation and spectral properties of quantum walks in electric fields

  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},
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… 

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