The mathematical design of a realistic three-position quantum switch controlled by the classical electric field is suggested in form of a circular quantum well - a unit disc on a plane- with four straight channels attached to it.This device implements a triple splitting of an input waveguide. The magnitude of the constant electric field directed parallel to the disc may be defined such that rotation of this field in the plane of the device permits manipulation of the electron current through the triple splitting. The problem of calculating of the current through the switch is reduced to the construction of scattered waves for the Schr"{o}dinger operator on the corresponding composite domain with the homogeneous Dirichlet conditions on the boundary. The Dirichlet boundary conditions are found to correspond most closely to real experimental conditions on the boundary of a deep quantum well. Explicit expression for transmission coefficient from one channel to another is obtained. Technically the analysis of the corresponding infinitely-dimensional spectral problem is reduced to the analysis of a relevant finite-dimensional analytic matrix function. We estimate the errors that arise from replacement of infinite-dimensional operator by the finite matrix. Our main result is the calculation of the working point of the switch in the multi-dimensional space of the numerical parameters of the switch which permits the resonance manipulation of the current. |
Keywords
Dirichlet0to-Neumann map, Scattering
Math Review Classification
Primary 35-XX
; Secondary &)-XX
Last Updated
16.11.01
Length
32 p
Availability
No online versions are available,
but there should be a hardcopy version available from the department.