On the quantum CTRW approach
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The concept of continuous-time random walk is generalized into the quantum approach using a completely positive map. This approach introduces in a phenomenological way the concept of disorder in the transport problem of a quantum open system. If the waiting-time of the continuous-time renewal approach is exponential we recover a semigroup for a dissipative quantum walk. Two models of non-Markovian evolution have been solved considering different types of waiting-time functions.