Nonanomalous heat transport in a one-dimensional composite chain

Abstract

Translation-invariant low-dimensional systems are known to exhibit anomalous heat transport. However, there are systems, such as the coupled-rotor chain, where translation invariance is satisfied, yet transport remains diffusive. It has been argued that the restoration of normal diffusion occurs due to the impossibility of defining a global stretch variable with a meaningful dynamics. In this Letter, an alternative mechanism is proposed, namely, that the transition to anomalous heat transport can occur at a scale that, under certain circumstances, may diverge to infinity. To illustrate the mechanism, I consider the case of a composite chain that conserves local energy and momentum as well as global stretch, and at the same time obeys, in the continuum limit, Fourier's law of heat transport. It is shown analytically that for vanishing elasticity the stationary temperature profile of the chain is linear; for finite elasticity, the same property holds in the continuum limit.

arXiv comment7 pages 1 figure; supplemental material included

References in corpus (15)

• Thermal conduction in classical low-dimensional lattices
• Heat Transport in low-dimensional systems
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• Anomalous heat conduction in one dimensional momentum-conserving systems
• Nonlinear fluctuating hydrodynamics for anharmonic chains
• Finite thermal conductivity in 1d lattices
• A momentum conserving model with anomalous thermal conductivity in low dimension
• Momentum conservation implies anomalous energy transport in 1d classical lattices
• Fourier's Law for a Harmonic Crystal with Self-consistent Stochastic Reservoirs
• Too Close to Integrable: Crossover from Normal to Anomalous Heat Diffusion
• A stochastic model of anomalous heat transport: analytical solution of the steady state
• Non-Fourier heat transport in nanosystems
• Eulerian and Lagrangian pictures of non-equilibrium diffusions
• Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas
• Long range correlations in stochastic transport with energy and momentum conservation