Green function approach for general quantum graphs
Alexandre G. M. Schmidt, Bin Kang Cheng, M. G. E. da Luz
We present a recursive prescription to calculate the exact Green function for general quantum graphs. For the closed case, the expression for the poles of G —which gives the individual eigenstates—has the structure of a semiclassical formula, where the sum over the periodic orbit is already performed. As applications we discuss eigenstate localization for a three-arm closed star and filter-like mechanisms for transmission throughout an open trident graph.
Journal of Physics A Mathematical and General•Oct 8, 2003•28 citations