Energy transport in the presence of long-range interactions

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.

7 pages, 6 figures

References in corpus (4)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Heat Transport in low-dimensional systems
• Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport

Cited by in corpus (9)

• Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
• Heat transport in long-ranged anharmonic oscillator models
• Heat conduction in chains of non-locally coupled harmonic oscillators: mean-field limit
• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain
• Superballistic and superdiffusive scaling limits of stochastic harmonic chains with long-range interactions
• Energy diffusion in the long-range interacting spin systems
• A family of fractional diffusion equations derived from stochastic harmonic chains with long-range interactions
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths
• Subdiffusive Energy Transport and Antipersistent Correlations Due to the Scattering of Phonons and Discrete Breathers