Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion

Abstract

Energy transport in one-dimensional chains of particles with three conservation laws is generically anomalous and belongs to the Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples where an apparent normal heat diffusion is found over a large range of length scales were reported. We propose a novel physical explanation of these intriguing observations. We develop a scaling analysis that explains how this may happen in the vicinity of an integrable limit, such as, but not only, the famous Toda model. In this limit, heat transport is mostly supplied by quasiparticles with a very large mean free path l. Upon increasing the system size L, three different regimes can be observed: a ballistic one, an intermediate diffusive range, and, eventually, the crossover to the anomalous (hydrodynamic) regime. Our theoretical considerations are supported by numerical simulations of a gas of diatomic hard-point particles for almost equal masses and of a weakly perturbed Toda chain. Finally, we discuss the case of the perturbed harmonic chain, which exhibits a yet different scenario.

Ultrahigh Convergent Thermal Conductivity of Carbon Nanotubes from Comprehensive Atomistic Modeling

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Thermal Conductivity of Rotator Chains with a Double-Barrier Interaction Potential

“…Research in this area has led to the discovery of a number of fundamental phenomena [7]; nevertheless, the problem of thermal conductivity remains open even with regard to one-dimensional model systems. This problem has been the subject of many articles and reviews [8][9][10], in which various types of interaction potentials and/or various boundary conditions were investigated. Even in the first numerical experiments, it was shown that the thermal conductivity coefficient of one-dimensional chains with an anharmonic interaction potential depends on the temperature and chain length and usually diverges in the limit of infinitely long chains.…”

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