Aspects of the disordered harmonic chain

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.