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

TL;DR

This paper investigates heat transport in a disordered classical anharmonic chain, revealing a transition from conducting to localized behavior influenced by disorder and chaos, with implications for understanding many-body localization phenomena.

Contribution

It provides a detailed numerical study of transport and chaos in a disordered nonlinear chain, proposing a novel exponential form for conductivity decay and analyzing boundary effects and chaos growth regimes.

Findings

Conductivity saturates to a finite value at large system size.

Conductivity decays faster than any power law as temperature approaches zero.

Chaos growth differs between weak and strong regimes, affecting transport properties.

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 ($N$) systems, saturates to a value $\kappa_\infty >0$ 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 $(T/\Delta) \to 0$ limit, and find that the form $\kappa_\infty \sim e^{-B |\ln(C \Delta/T)|^3}$ fits our data. This form has earlier been suggested by a theory based on the dynamics of multi-oscillator chaotic islands. The finite-size effect can be $\kappa_N < \kappa_{\infty}$ due to boundary resistance when the bulk conductivity is high (the weak disorder case), or $\kappa_N > \kappa_{\infty}$ 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.