Modeling Quantum Dot Systems as Random Geometric Graphs with Probability Amplitude-Based Weighted Links

This paper focuses on modeling a disorder ensemble of quantum dots (QDs) as a special kind of Random Geometric Graphs (RGG) with weighted links. We compute any link weight as the overlap integral (or electron probability amplitude) between the QDs (=nodes) involved. This naturally leads to a weighted adjacency matrix, a Laplacian matrix, and a time evolution operator that have meaning in Quantum Mechanics. The model prohibits the existence of long-range links (shortcuts) between distant nodes because the electron cannot tunnel between two QDs that are too far away in the array. The spatial network generated by the proposed model captures inner properties of the QD system, which cannot be deduced from the simple interactions of their isolated components. It predicts the system quantum state, its time evolution, and the emergence of quantum transport when the network becomes connected.

Node-Block based Topology Control Algorithm for Mobile Optical Wireless Communication Networks

Topology control is an efficient strategy to improve robustness and connectivity in networks. The mobility of nodes, the limited node degree and fragile links in optical wireless communication (OWC) networks make topology control a great challenge. In this paper, the node-block (NB) based topology control algorithm is proposed. Firstly, the proposed algorithm uses the prediction of the contact time between the nodes as the link weight to form a stable tree structure that is called node-block; secondly, the quantized value based on Gamma-Gamma channel model is used as the link weight between node-blocks, and then a multi-link connection is established between any two node-blocks; finally, a connected graph is formed. The performance evaluation parameters, such as topological stability, algebraic connectivity and average node degree are discussed, and their expressions are given. The related simulations are carried out, and comparing with MST algorithm are also made. The results show that our proposed topology control algorithm can ensure the connectivity and stability of the OWC networks, meanwhile, the available node degree are reserved is applied to the large-scale networks.