Possible construction of a quantum multiplexer

The problem of constructing a quantum multiplexer is discussed. A possible construction based on the properties of quantum waveguides connected with a quantum resonator is considered. A descriptive model of ballistic transport in 1D-2D-1D system is suggested. It is analogous to the zero-range potential method and based on the theory of self-adjoint extensions of symmetric operators. A general formula for transmission coefficient for the system, particularly in the case of presence of a magnetic field, is obtained. A concrete realization of the formula for the quantum system in question is developed and analyzed. Quantum resonators with two and four leads are studied. A possible application of the result for constructing a quantum multiplexer is discussed. Control parameters for the device are electron energy ("momentum filter") or bias voltage related with the radius of the quantum resonator ("multiplexer"). If there is a magnetic field then a value of a magnetic field B is an additional control parameter.