# Narrow peaks of full transmission in simple quantum graphs

## TL;DR

This paper investigates quantum graphs with degree-3 vertices, identifying conditions for full transmission and suppression, including narrow peaks caused by quantum interference, with potential applications in quantum device control.

## Contribution

It introduces specific configurations of simple quantum graphs that exhibit narrow transmission peaks and suppression windows, advancing understanding of quantum interference effects in these structures.

## Key findings

- Identified regions of full transmission and suppression in diamond and hexagonal graphs.
- Discovered narrow peaks of full transmission due to constructive interference.
- Analyzed series and parallel graph arrangements for controlled quantum transmission.

## Abstract

This work deals with quantum graphs, focusing on the transmission properties they engender. We first select two simple diamond graphs, and two hexagonal graphs in which the vertices are all of degree 3, and investigate their transmission coefficients. In particular, we identified regions in which the transmission is fully suppressed. We also considered the transmission coefficients of some series and parallel arrangements of the two basic graphs, with the vertices still preserving the degree 3 condition, and then identified specific series and parallel compositions that allow for windows of no transmission. Inside some of these windows, we found very narrow peaks of full transmission, which are consequences of constructive quantum interference. Possibilities of practical use as the experimental construction of devices of current interest to control and manipulate quantum transmission are also discussed.