Resonance Triadic Quantum Switch

A. Mikhailova, B. Pavlov


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.

Dirichlet0to-Neumann map, Scattering

Math Review Classification
Primary 35-XX ; Secondary &)-XX

Last Updated

32 p

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