Multi-particle scattering and breakdown of the Wiedemann-Franz law at a junction of N interacting quantum wires

TL;DR

This paper investigates charge and thermal transport at a junction of interacting quantum wires, revealing how multi-particle scattering leads to the breakdown of the Wiedemann-Franz law, with implications for quantum transport in Luttinger liquids.

Contribution

It provides a detailed analysis of the thermal conductance and the conditions under which the Wiedemann-Franz law fails at quantum wire junctions, highlighting the role of multi-particle scattering.

Findings

Breakdown of Wiedemann-Franz law at quantum wire junctions.

Identification of trivial and junction-related violations.

Impact of external reservoirs on conductance tensors.

Abstract

We analyze the charge and thermal transport at a junction of interacting quantum wires close to equilibrium. Within the framework of Tomonaga-Luttinger liquids, we compute the thermal conductance for a wide class of boundary conditions and detail the physical processes leading to the breakdown of the Wiedemann-Franz law at the junction. We show how connecting external reservoirs to the quantum wires affects the conductance tensors close to the various fixed points of the phase diagram of the junction. We therefore distinguish two types of violation of the Wiedemann-Franz law: a "trivial" one, independent of the junction dynamics and arising from the breakdown of the Fermi-liquid picture in the wire, and a junction-related counterpart, arising from multi-particle scattering processes at the junction.