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.

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

References in corpus (13)

• 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
• 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
• Anomalous heat transport in classical many-body systems: overview and perspectives
• Thermal transport in the Fermi-Pasta-Ulam model with long-range interactions
• Energy transport in the presence of long-range interactions
• 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

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• 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