Conductance scaling of junctions of Luttinger-liquid wires out of equilibrium

TL;DR

This paper develops a renormalization group theory for the conductance of multi-lead Luttinger-liquid junctions out of equilibrium, revealing how conductances scale with bias voltages.

Contribution

It introduces a second-order perturbative renormalization group framework for analyzing conductance scaling in multi-lead Luttinger-liquid junctions out of equilibrium.

Findings

Conductances obey scaling laws derived from RG beta functions.

Second-order perturbation results provide detailed RG flow equations.

The theory applies to N-lead junctions with bias voltages.

Abstract

We develop the renormalization group theory of the conductances of N-lead junctions of spinless Luttinger-liquid wires as functions of bias voltages applied to N independent Fermi-liquid reservoirs. Based on the perturbative results up to second order in the interaction we demonstrate that the conductances obey scaling. The corresponding renormalization group $\beta$ functions are derived up to second order.