Dimensionality reduction in translational noninvariant wave guides

TL;DR

This paper introduces a method to simplify the analysis of translational noninvariant wave guides by reducing them to 1D lines, preserving low-energy properties and facilitating the study of complex structures like quantum wire networks.

Contribution

It proposes a novel scheme to reduce complex wave guides into simpler 1D models, applicable to guides with discontinuities and low-energy conditions.

Findings

Scheme effectively simplifies wave guide analysis

Applicable when discontinuities are distant and energy is low

Potential use in quantum wire network studies

Abstract

A scheme to reduce translational noninvariant quasi-one-dimensional wave guides into singly or multiply connected one-dimensional (1D) lines is proposed. It is meant to simplify the analysis of wave guides, with the low-energy properties of the guides preserved. Guides comprising uniform-cross-sectional sections and discontinuities such as bends and branching junctions are considered. The uniform sections are treated as 1D lines, and the discontinuities are described by equations sets connecting the wave functions on the lines. The procedures to derive the equations and to solve reduced systems are illustrated by examples, and the scheme is found to apply when the discontinuities are distant and the energy is low. When the scheme applies, it may substantially simplify the analysis of a wave guide, and hence the scheme may find uses in the study of related problems, such as quantum wire networks.