Dimensionality reduction in translational noninvariant wave guides
arXiv:0809.2122 · doi:10.1016/j.physe.2008.09.018
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.
17 pages, 5 figures
References in corpus (7)
- Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
- Spintronic single qubit gate based on a quantum ring with spin-orbit interaction
- Rashba effect induced localization in quantum networks
- Effect of spin-orbit coupling on zero-conductance resonances in asymmetrically coupled one-dimensional rings
- Magnetoconductance properties of rectangular arrays of spintronic quantum rings
- Connecting wave functions at a three-leg junction of one-dimensional channels
- Quantum current magnification in a multi-channel mesoscopic ring