A model of a quantum waveguide multiplexer

Abstract

The paper explores the system of quantum waveguides and resonators. It suggests a solvable model of zero-width coupling windows based on the operator extensions theory in the Pontryagin space with indefinite metrics. The model self-adjoint operator is constructed explicitly, and it is similar (in some sense) to that of a physical system. We obtain an expression for the transmission coefficient for electrons and investigate its dependence on the electron energy which has a resonant character. It allows to control the electron transmission to different waveguides. The paper proposes a model of a three-channel quantum mesoscopic multiplexer.