Coherent transport in multi-branch circuits

TL;DR

This paper analyzes coherent electron transport in multi-branch quantum circuits, identifying conditions for localized states and examining their impact on signal transmission, including effects of disorder and super-radiant transitions.

Contribution

It provides analytical conditions for localized states in multi-branch circuits and studies their role in transport, incorporating effects of disorder and super-radiant phenomena.

Findings

Localized states can be analytically predicted in closed circuits.

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

Localized states remain robust under certain disorder conditions.

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 and find an analytical estimate, confirmed by numerical data, for the robustness of the isolated states and their role in transport processes.