# Quantum Reflection and Transmission in Ring Systems with Double Y-Junctions: Occurrence of Perfect Reflection

## TL;DR

This paper develops a new formalism for analyzing quantum scattering in ring systems with double Y-junctions, revealing conditions for perfect reflection that differ from traditional one-dimensional systems.

## Contribution

It introduces a path integral-based approach for quantum scattering in ring systems with double Y-junctions and uncovers conditions for perfect reflection in anti-symmetric configurations.

## Key findings

- Perfect reflection can occur in anti-symmetric ring systems.
- New compact formulas for probability amplitudes are derived.
- Quantum reflection and transmission depend on junction symmetry.

## Abstract

We consider the scattering problems of a quantum particle in a system with a single Y-junction and in ring systems with double Y-junctions. We provide new formalism for such quantum mechanical problems. Based on a path integral approach, we find compact formulas for probability amplitudes in the ring systems. We also discuss quantum reflection and transmission in the ring systems under scale-invariant junction conditions. It is remarkable that perfect reflection can occur in an anti-symmetric ring system, in contrast with the one-dimensional quantum systems having singular nodes of degree 2.