Power dissipation for systems with junctions of multiple quantum wires

TL;DR

This paper develops a unified framework to analyze power dissipation at junctions of multiple quantum wires, applicable to both interacting and non-interacting electrons, and explores models based on quantum Hall edge states.

Contribution

It introduces a method to characterize dissipation using the eigenvalues of M^T M and applies it to models involving quantum Hall edge states.

Findings

Eigenvalues of M^T M determine dissipation levels.

Eigenvectors identify bias voltage configurations for maximum dissipation.

Models based on quantum Hall edge states realize specific M-matrices.

Abstract

We study power dissipation for systems of multiple quantum wires meeting at a junction, in terms of a current splitting matrix (M) describing the junction. We present a unified framework for studying dissipation for wires with either interacting electrons (i.e., Tomonaga-Luttinger liquid wires with Fermi liquid leads) or non-interacting electrons. We show that for a given matrix M, the eigenvalues of M^T M characterize the dissipation, and the eigenvectors identify the combinations of bias voltages which need to be applied to the different wires in order to maximize the dissipation associated with the junction. We use our analysis to propose and study some microscopic models of a dissipative junction which employ the edge states of a quantum Hall liquid. These models realize some specific forms of the M-matrix whose entries depends on the tunneling amplitudes between the different edges.