Heat transport in long-ranged Fermi-Pasta-Ulam-Tsingou-type models.

Abstract

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 δ≥0. For such a nonintegrable model, one of the recent results that has captured quite some attention is the puzzling ballisticlike transport observed for δ=2, reminiscent of integrable systems. Here, we first employ the reverse nonequilibrium molecular dynamics simulations to look closely at the δ=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 δ=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 ballisticlike transport properties can be consistently explained in terms of a novel depinning of the discrete breathers that makes them highly mobile at δ=2. Finally, in the presence of quartic pinning potentials we find that the long-ranged model exhibits Fourier (diffusive) transport at δ=2, as one would expect from short-ranged interacting systems with broken momentum conservation. Such a diffusive regime is not observed for harmonic pinning.