# Plasmon localization and relaxation, and thermal transport in one-dimensional conductors

## TL;DR

This paper investigates the localization, decay, and thermal transport of one-dimensional plasmons in a disordered Luttinger liquid, revealing how decay rates and thermal conductance scale with frequency and system size.

## Contribution

It introduces a detailed analysis of plasmon decay and thermal conductance in disordered 1D conductors, including many-body localization effects and size-dependent scaling laws.

## Key findings

- Decay rate of plasmons varies with frequency, showing crossover behavior.
- Thermal conductance scales as L^{-1/2} for short wires and L^{-2/3} for longer wires.
- Many-body localization suppresses plasmon decay at high frequencies.

## Abstract

We study the localization and decay properties as well as the thermal conductance of one-dimensional plasmons. Our model contains a Luttinger-liquid part with spatially random plasmon velocity and interaction parameter as well as a nonlinearity that is cubic in density. The scaling of the decay rate of plasmons is obtained in several regimes. At sufficiently high frequencies, it describes the inelastic life time of localized plasmon excitations that crosses over to the clean result with lowering frequencies. For higher frequencies, we analyze implications of many-body-localization effects that lead to a suppression of the decay rate. We find that the thermal conductance depends in a non-trivial fashion on the system size $L$. Specifically, it scales as $L^{-1/2}$ for sufficiently short wires and crosses over to $L^{-2/3}$ scaling for longer wires.