Abstract
In this work a Green-function approach for scattering quantum walks is developed. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression for arbitrary topologies and position-dependent quantum amplitudes. By introducing the step and path operators, it is shown how to extract any information about the system from the Green function. The method's relevant features are demonstrated by discussing in detail an example, a general diamond-shaped graph.
- Received 14 July 2011
DOI:https://doi.org/10.1103/PhysRevA.84.042343
©2011 American Physical Society
