Energy transport in the presence of long-range interactions

TL;DR

This paper investigates energy transport in long-range interacting models, revealing subdiffusive behavior in the HMF model and superdiffusion with added interactions, explained by localized excitation modes and applicable to various models.

Contribution

It demonstrates how long-range interactions influence energy diffusion, introducing localized modes as a key factor, and extends findings to generic models with algebraic decay of interactions.

Findings

HMF model exhibits subdiffusive energy transport, acting as a thermal insulator.

Adding nearest neighbor interactions induces superdiffusive energy transport.

Energy localization via discrete breathers explains the observed transport behaviors.

Abstract

We study energy transport in the paradigmatic Hamiltonian mean-field (HMF) model and other related long-range interacting models using molecular dynamics simulations. We show that energy diffusion in the HMF model is subdiffusive in nature, which confirms a recently obtained intriguing result that, despite being globally interacting, this model is a thermal insulator in the thermo- dynamic limit. Surprisingly, when additional nearest neighbor interactions are introduced to the HMF model, an energy superdiffusion is observed. We show that these results can be consistently explained by studying energy localization due to thermally generated intrinsic localized excitation modes (discrete breathers) in nonlinear discrete systems. Our analysis for the HMF model can also be readily extended to more generic long-range interacting models where the interaction strength decays algebraically with the (shortest) distance between two lattice sites. This reconciles many of the apparently counter-intuitive results presented recently [C. Olivares and C. Anteneodo, Phys. Rev. E 94, 042117 (2016); D. Bagchi, Phys. Rev. E 95, 032102 (2017)] concerning energy transport in two such long-range interacting models.