Hydrodynamics and transport in the long-range-interacting φ4 chain. (1st March 2022)

• Record Type: Journal Article
• Authors: Iubini, Stefano; Lepri, Stefano; Ruffo, Stefano
• Is Part Of: Journal of statistical mechanics. (2022:Mar.)
• Publication Date: 2022-03-01
• Subjects: correlation functions -- fluctuating hydrodynamics -- heat conduction -- numerical simulations; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ac59b6
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We present a simulation study of the one-dimensional φ 4 lattice theory with long-range interactions decaying as an inverse power r −(1+ σ ) of the intersite distance r, σ > 0. We consider the cases of single and double-well local potentials with both attractive and repulsive couplings. The double-well, attractive case displays a phase transition for 0 < σ ⩽ 1 analogous to the Ising model with long-range ferromagnetic interactions. A dynamical scaling analysis of both energy structure factors and excess energy correlations shows that the effective hydrodynamics is diffusive for σ > 1 and anomalous for 0 < σ < 1, where fluctuations propagate superdiffusively. We argue that this is accounted for by a fractional diffusion process and we compare the results with an effective model of energy transport based on Lévy flights. Remarkably, this result is fairly insensitive on the phase transition. Nonequilibrium simulations with an applied thermal gradient are in quantitative agreement with the above scenario.