CONSTRUÇÃO DA FUNÇÃO DE GREEN EXATA PARA GRAFOS QUÃNTICOS UTILIZANDO A MATRIZ DE ADJACÊNCIA

Abstract

In this work we review the diferent distinct aspects associated with quantum dynamics in graphs. The approach used is that of the Green's functions, dened in the feld of energy. In this technique the Green's functions are obtained through the sum of all possible classical paths connecting the initial and Final points, the style of Feynman path integrals. Local quantum efects are included through the use of quantum amplitudes for reection and transmission are defined in each of the vertices of the graph. We show that in order to get the exact Green function can use the adjacency matrix of the graph, which sets the links between the vertices of the graph. This approach ensures that all paths have been accounted for and has the advantage of providing a rating only for the various families of paths that can be defined in a given graph. An application of the method to study resonances in graphs is also presented.