Aspects of the disordered harmonic chain

TL;DR

This paper analyzes the disordered harmonic chain's thermal and dynamical properties, focusing on Lyapunov exponents, heat current, and fluctuation theorems, providing detailed calculations and a comprehensive review of existing methods.

Contribution

It introduces a combined disorder model for mass and coupling strength and applies advanced theoretical methods to analyze heat transport and fluctuations.

Findings

Mass and coupling disorder can be combined into a renormalized mass disorder.

The approach to disorder-averaged heat current is reviewed and applied.

The validity of the Gallavotti-Cohen fluctuation theorem is discussed.

Abstract

We discuss the driven harmonic chain with fixed boundary conditions subject to weak coupling strength disorder. We discuss the evaluation of the Liapunov exponent in some detail expanding on the dynamical system theory approach by Levi et al. We show that including mass disorder the mass and coupling strength disorder can be combined in a renormalised mass disorder. We review the method of Dhar regarding the disorder-averaged heat current, apply the approach to the disorder-averaged large deviation function and finally comment on the validity of the Gallavotti-Cohen fluctuation theorem. The paper is also intended as an introduction to the field and includes detailed calculations.