Heat transport in long-ranged anharmonic oscillator models

Abstract

In this work, we perform a detailed study of heat transport in one dimensional long-ranged anharmonic oscillator systems, such as the long-ranged Fermi-Pasta-Ulam-Tsingou model. For these systems, the long-ranged anharmonic potential decays with distance as a power-law, controlled by an exponent $\delta \ge 0$. For such a non-integrable model, one of the recent results that has captured quite some attention is the puzzling ballistic-like transport observed for $\delta =2$, reminiscent of integrable systems. Here, we first employ the reverse nonequilibrium molecular dynamics simulations to look closely at the $\delta =2$ transport in three long-ranged models, and point out a few problematic issues with this simulation method. Next, we examine the process of energy relaxation, and find that relaxation can be appreciably slow for $\delta =2$ in some situations. We invoke the concept of nonlinear localized modes of excitation, also known as discrete breathers, and demonstrate that the slow relaxation and the ballistic-like transport properties can be consistently explained in terms of a novel depinning of the discrete breathers that makes them highly mobile at $\delta =2$. Finally, in the presence of quartic pinning potentials we find that the long-ranged model exhibits Fourier (diffusive) transport at $\delta =2$, as one would expect from short-ranged interacting systems with broken momentum conservation. Such a diffusive regime is not observed for harmonic pinning.

arXiv comment14 pages total, 10 pages main paper, 4 pages Appendix, 6 main figures, 8 supplementary figures

References in corpus (29)

• Thermal conduction in classical low-dimensional lattices
• Discrete Breathers
• Statistical mechanics and dynamics of solvable models with long-range interactions
• Length-dependent thermal conductivity in suspended single-layer graphene
• Heat Transport in low-dimensional systems
• Nonequilibrium Statistical Mechanics of Systems with Long-Range Interactions: Ubiquity of Core-Halo Distributions
• Thermodynamics and dynamics of systems with long-range interactions
• Mobility and Reactivity of Discrete Breathers
• Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems
• Abundance of regular orbits and out-of-equilibrium phase transitions in the thermodynamic limit for long-range systems
• Movability of Localized Excitations in Nonlinear Discrete Systems - a Separatrix Problem
• Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
• Anomalous heat transport in classical many-body systems: overview and perspectives
• Increasing thermal rectification: Effects of long range interactions
• Heat transport in oscillator chains with long-range interactions coupled to thermal reservoirs
• Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions
• Dynamical freezing of relaxation to equilibrium
• Role of the range of the interactions in thermal conduction
• Thermal transport in long-range interacting Fermi-Pasta-Ulam chains
• Cooling nonlinear lattices toward localisation
• Sensitivity to initial conditions of a $d$-dimensional long-range-interacting quartic Fermi-Pasta-Ulam model: Universal scaling
• Energy current correlation in solvable long-range interacting systems
• Energy transport in the presence of long-range interactions
• Transport in perturbed classical integrable systems: the pinned Toda chain
• Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model
• Chaos and localization in the Discrete Nonlinear Schrödinger Equation
• Transport properties of the classical Toda chain: effect of a pinning potential
• Construction of nonlinear lattice with potential symmetry for smooth propagation of discrete breather
• Soliton solutions of Calogero model in harmonic potential

Cited by in corpus (8)

• Non-Fourier heat transport in nanosystems
• Heat conduction in chains of non-locally coupled harmonic oscillators: mean-field limit
• Heat transport in nonlinear lattices free from the Umklapp process
• Non-equilibrium steady states of long-range coupled harmonic chains
• Conformal order and Poincar$\acute{\mathrm{e}}$-Klein mapping underlying electrostatics-driven inhomogeneity in tethered membranes
• Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths
• Construction of cubic nonlinear lattice free from umklapp processes