Coherent quantum transport in a star graph

TL;DR

This paper analyzes coherent quantum transport in a multi-branch star graph circuit, deriving conditions for localized states, studying signal transmission with non-Hermitian Hamiltonians, and examining effects of disorder.

Contribution

It provides analytical conditions for localized states, explores super-radiant transition in open systems, and investigates disorder effects in quantum transport on star graphs.

Findings

Localized states emerge under specific conditions.

Super-radiant transition occurs when level width matches level spacing.

Disorder impacts transmission properties significantly.

Abstract

A multi-branch quantum circuit is considered from the viewpoint of coherent electron or wave transport. Starting with the closed system, we give analytical conditions for the appearance of two isolated localized states out of the energy band. In the open system, using the method of the effective non-Hermitian Hamiltonian, we study signal transmission through such a circuit. The super-radiant transition occurs when the average level width becomes comparable to the mean level spacing.We consider also the case with on-site disorder.