Dimerized decomposition of quantum evolution on an arbitrary graph

The study of quantum evolution on graphs for diversified topologies is beneficial to modeling various realistic systems. A systematic method, the dimerized decomposition, is proposed to analyze the dynamics on an arbitrary network. By introducing global “flows” among interlinked dimerized subsystems, each of which locally consists of an input and an output port, the method provides an intuitive picture that the local properties of the subsystem are separated from the global structure of the network. The pictorial interpretation of quantum evolution as multiple flows through the graph allows for the analysis of the complex network dynamics supplementary to the conventional spectral method. Using the decomposition, the relation between spectral coefficients of adjacent sites with regard to individual dimer is obtained.