Anomalous conduction and second sound in the Fermi-Pasta-Ulam-Tsingou chain: wave-turbulence approach

TL;DR

This paper investigates anomalous thermal conduction and second sound in the Fermi-Pasta-Ulam-Tsingou chain using a wave kinetic equation approach, revealing the interplay of phonons at different scales and their transport behaviors.

Contribution

It applies the spatially nonhomogeneous wave kinetic equation to the FPUT model, elucidating the mechanisms behind anomalous conduction and second sound phenomena.

Findings

Anomalous conductivity scaling due to high and low wavenumber interplay

High-wavenumber phonons relax diffusively, following Fourier law

Low-wavenumber phonons transfer energy ballistically, akin to second sound

Abstract

One-dimensional particle chains are fundamental models to explain anomalous thermal conduction in low-dimensional solids like nanotubes and nanowires. In these systems the thermal energy is carried by phonons, i.e. propagating lattice oscillations that interact via nonlinear resonance. The average energy transfer between the phonons is described by the wave kinetic equation (WKE), derived directly from the microscopic dynamics. Here, we use the spatially nonhomogeneous WKE of the prototypical $\beta-$ Fermi-Pasta-Ulam-Tsingou (FPUT) model, equipped with thermostats able to set different temperatures at the two ends. Our main findings are as follows: (i) The anomalous scaling of the conductivity with the system size, in close agreement with the known results from the microscopic dynamics, is due to a nontrivial interplay between high and low wavenumbers. (ii) The high-wavenumber phonons relax to local thermodynamic equilibrium transporting energy diffusively, {\it \`a la Fourier}. (iii) The low-wavenumber phonons are nearly noninteracting and transfer energy ballistically; this latter phenomenon is the analogous of the second sound emission, observed for example in superfluids.