Underlying mechanisms for normal heat transport in one-dimensional anharmonic oscillator systems with a double-well interparticle interaction

Abstract

Previous studies have suggested a crossover from superdiffusive to normal heat transport in one-dimensional (1D) anharmonic oscillator systems with a double-well type interatomic interaction like $V(\xi )=-{\xi }^2/2+{\xi }^4/4$, when the system temperature is varied. In order to better understand this unusual manner of thermal transport, here we perform a direct dynamics simulation to examine how the spreading processes of the three physical quantities, i.e., the heat, the total energy and the momentum, would depend on temperature. We find three main points that are worth noting: (i) The crossover from superdiffusive to normal heat transport is well verified from a new perspective of heat spread; (ii) The spreading of the total energy is found to be very distinct from heat diffusion, especially that under some temperature regimes, energy is strongly localized, while heat can be superdiffusive. So one should take care to derive a general connection between the heat conduction and energy diffusion; (iii) In a narrow range of temperatures, the spreading of momentum implies clear unusual non-ballistic behaviors; however, such unusual transport of momentum cannot be directly related to the normal transport of heat. An analysis of phonons spectra suggests that one should also take the effects of phonons softening into account. All of these results may provide insights into establishing the connection between the macroscopic heat transport and the underlying dynamics in 1D systems.

18 pages, 14 figures

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• Using Hilbert transform and classical chains to simulate quantum walks
• Anomalous temperature-dependent heat transport in one-dimensional momentum-conserving systems with soft-type interparticle interaction
• Heat perturbations spreading in the Fermi-Pasta-Ulam-$\beta$ system with next-nearest-neighbor coupling: Competition between phonon dispersion and nonlinearity
• KPZ modes in $d$-dimensional directed polymers
• Temperature dependent divergence of thermal conductivity in momentum conserving 1D lattice with asymmetric potential