Connecting wave functions at a three-leg junction of one-dimensional channels

Abstract

We propose a scheme to connect the wave functions on different one-dimensional branches of a three-leg junction (Y-junction). Our scheme differs from that due to Griffith [Trans. Faraday Soc. 49, 345 (1953)] in the respect that ours can model the difference in the widths of the quasi-one-dimensional channels in different systems. We test our scheme by comparing results from a doubly-connected one-dimensional system and a related quasi-one-dimensional system, and we find a good agreement. Therefore our scheme may be useful in the construction of one-dimensional effective theories out of (multiply-connected) quasi-one-dimensional systems.

6 pages, 4 figures

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• Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
• Spin-dependent (magneto)transport through a ring due to spin-orbit interaction
• Spintronic single qubit gate based on a quantum ring with spin-orbit interaction
• Rashba effect induced localization in quantum networks
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Cited by in corpus (6)

• Aharonov-Bohm oscillations in a mesoscopic ring with asymmetric arm-dependent injection
• Localized states in the continuum in low-dimensional systems
• A quantum-network approach to spin interferometry driven by Abelian and non-Abelian fields
• Dimensionality reduction in translational noninvariant wave guides
• Physical approach to quantum networks with massive particles
• Importance of individual scattering matrix elements at Fano resonances