Anomalous conduction in one-dimensional particle lattices: Wave-turbulence approach

Francesco De Vita, Giovanni Dematteis, Raffaele Mazzilli, Davide Proment, Yuri V. Lvov, and Miguel Onorato
Phys. Rev. E 106, 034110 – Published 7 September 2022

Abstract

One-dimensional particle chains are fundamental models to explain anomalous thermal conduction in low-dimensional solids such as 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 can be described by the wave kinetic equation, derived directly from the microscopic dynamics. Here we use the spatially nonhomogeneous wave kinetic equation of the prototypical β-Fermi-Pasta-Ulam-Tsingou model, to study thermal conduction in one-dimensional particle chains on a mesoscale description. By means of numerical simulations, we study two complementary aspects of thermal conduction: in the presence of thermostats setting different temperatures at the two ends and propagation of a temperature perturbation over an equilibrium background. 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 wave numbers. (ii) The high-wave-number phonons relax to local thermodynamic equilibrium transporting energy diffusively, in the manner of Fourier. (iii) The low-wave-number phonons are nearly noninteracting and transfer energy ballistically. These results present perspectives for the applicability of the full nonhomogeneous wave kinetic equation to study thermal propagation.

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  • Received 4 April 2022
  • Accepted 13 July 2022

DOI:https://doi.org/10.1103/PhysRevE.106.034110

©2022 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsCondensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Francesco De Vita1, Giovanni Dematteis2,*, Raffaele Mazzilli3, Davide Proment4, Yuri V. Lvov2, and Miguel Onorato5,6

  • 1DMMM, Politecnico di Bari, Via Re David 200, Bari 70125, Italy
  • 2Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180, USA
  • 3Max-Planck-Institut für Festkörperforschung, 70569 Stuttgart, Germany
  • 4School of Mathematics, University of East Anglia, Norwich Research Park, NR4 7TJ Norwich, United Kingdom
  • 5Dipartimento di Fisica, Università di Torino, Via P. Giuria 1, Torino 10125, Italy
  • 6INFN, Sezione di Torino, Via P. Giuria 1, Torino 10125, Italy

  • *Corresponding author: giovannidematteis@gmail.com

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Issue

Vol. 106, Iss. 3 — September 2022

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