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In this paper, we consider the quantum-mechanical phase space patterns onordered and disordered networks. For ordered networks in which each node isconnected to its 2m nearest neighbors (m on either side), the phase spacequasi-probability of Wigner function shows various patterns. In the long timelimit, on even-numbered networks, we find an asymmetric quasi-probabilitybetween the node and its opposite node. This asymmetry depends on the networkparameters and specific phase space positions. For disordered networks in whicheach edge is rewired with probability p>0, the phase space displays regionallocalization on the initial node.

Phase space patterns of quantum transport on ordered and disordered networks