Phase space patterns of quantum transport on ordered and disordered   networks
  In this paper, we consider the quantum-mechanical phase space patterns on ordered and disordered networks. For ordered networks in which each node is connected to its 2m nearest neighbors (m on either side), the phase space quasi-probability of Wigner function shows various patterns. In the long time limit, on even-numbered networks, we find an asymmetric quasi-probability between the node and its opposite node. This asymmetry depends on the network parameters and specific phase space positions. For disordered networks in which each edge is rewired with probability p>0, the phase space displays regional localization on the initial node. 
Xinping Xu, Feng Liu