In this work we study certain aspects of Open Quantum Random Walks (OQRWs), aclass of quantum channels described by S. Attal et al. \cite{attal}. As a firstobjective we consider processes which are nonhomogeneous in time, i.e., at eachtime step, a possibly distinct evolution kernel. Inspired by a spectraltechnique described by L. Saloff-Coste and J. Z\'u\~niga \cite{saloff}, wedefine a notion of ergodicity for finite nonhomogeneous quantum Markov chainsand describe a criterion for ergodicity of such objects in terms of singularvalues. As a second objective, and based on a quantum trajectory approach, westudy a notion of hitting time for OQRWs and we see that many constructions arevariations of well-known classical probability results, with the density matrixdegree of freedom on each site giving rise to systems which are seen to benonclassical. In this way we are able to examine open quantum versions of thegambler's ruin, birth-and-death chain and a basic theorem on potential theory.
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