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

TL;DR

This paper introduces a new scheme for connecting wave functions at a three-leg junction in one-dimensional channels, accommodating differences in channel widths, and validates it through comparison with related systems.

Contribution

The authors develop a novel scheme for wave function connection at Y-junctions that accounts for varying channel widths, improving upon previous models.

Findings

Good agreement between the scheme and system simulations

Potential usefulness in constructing effective one-dimensional theories

Enhanced modeling of quasi-one-dimensional systems

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.