Transport, correlations, and chaos in a classical disordered anharmonic chain

Abstract

We explore transport properties in a disordered nonlinear chain of classical harmonic oscillators, and thereby identify a regime exhibiting behavior analogous to that seen in quantum many-body-localized systems. Through extensive numerical simulations of this system connected at its ends to heat baths at different temperatures, we computed the heat current and the temperature profile in the nonequilibrium steady state as a function of system size N, disorder strength Delta, and temperature T. The conductivity kappa(N), obtained for finite length (N), saturates to a value kappa(infinity) > 0 in the large N limit, for all values of disorder strength Delta and temperature T > 0. We show evidence that for any Delta > 0 the conductivity goes to zero faster than any power of T in the (T/Delta) -> 0 limit, and find that the form kappa(infinity) similar to e(-B vertical bar ln(C Delta/T)vertical bar 3) fits our data. This form has earlier been suggested by a theory based on the dynamics of multioscillator chaotic islands. The finite-size effect can be kappa(N) < kappa(infinity) due to boundary resistance when the bulk conductivity is high (the weak disorder case), or kappa(N) > kappa(infinity) due to direct bath-to-bath coupling through bulk localized modes when the bulk is weakly conducting (the strong disorder case). We also present results on equilibrium dynamical correlation functions and on the role of chaos on transport properties. Finally, we explore the differences in the growth and propagation of chaos in the weak and strong chaos regimes by studying the classical version of the out-of-time-ordered commutator.