Quantum Star Graphs and Spectral Branching Filter

The analysis of quantum star graph, a mathematical model of quantum-wire based single electron device, is presented. It is shown that the proper connection condition of quantum wave functions at the node can be understood as combinations of ¿ and ¿' interactions between all pairs of lines. We examine the case of n = 2 and n = 3, and show that the identification of ¿ and ¿' components enables the designing of quantum spectral branching filters.