Green function approach for general quantum graphs
Alexandre G. M. SchmidtDepartamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-990, Curitiba, Paraná, BrazilBin ChengDepartamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-990, Curitiba, Paraná, BrazilM. G. E. da LuzDepartamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, 81531-990, Curitiba, Paraná, Brazil
2003en
ABI
Abstract
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.
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Cited by 20 references