Phase space patterns of quantum transport on ordered and disordered networks

TL;DR

This paper investigates quantum transport in ordered and disordered networks, revealing distinct phase space patterns, asymmetries, and localization effects influenced by network structure and parameters.

Contribution

It introduces analysis of quantum phase space patterns on both ordered and disordered networks, highlighting asymmetries and localization phenomena.

Findings

Ordered networks show asymmetric Wigner function patterns depending on network parameters.

Disordered networks exhibit regional localization around the initial node.

Asymmetry in phase space depends on network size and phase space position.

Abstract

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.