- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

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

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
PDF

Phys. Rev. E 106, 034110 – Published 7 September, 2022

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

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.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (45)

  1. J. B. J. Fourier, Théorie Analytique de la Chaleur (Didot, Paris, 1822).
  2. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics, edited by P. Fulde, Springer Series in Solid-State Sciences Vol. 31 (Springer, Berlin, 2012).
  3. Z. Rieder, J. Lebowitz, and E. Lieb, J. Math. Phys. 8, 1073 (1967).
  4. A. Dhar and K. Saito, in Thermal Transport in Low Dimensions: From Statistical Physics to Nanoscale Heat Transfer, edited by S. Lepri, Lecture Notes in Physics Vol. 921 (Springer, Berlin, 2016), pp. 39–105.
  5. S. Lepri, R. Livi, and A. Politi, Phys. Rep. 377, 1 (2003).
  6. D. Donadio and G. Galli, Phys. Rev. Lett. 102, 195901 (2009).
  7. C. W. Chang, D. Okawa, H. Garcia, A. Majumdar, and A. Zettl, Phys. Rev. Lett. 101, 075903 (2008).
  8. J. Chen, G. Zhang, and B. Li, Nano Lett. 10, 3978 (2010).
  9. S. Shen, A. Henry, J. Tong, R. Zheng, and G. Chen, Nat. Nanotechnol. 5, 251 (2010).
  10. N. Yang, G. Zhang, and B. Li, Nano Today 5, 85 (2010).
  11. S. Liu, X. Xu, R. Xie, G. Zhang, and B. Li, Eur. Phys. J. B 85, 337 (2012).
  12. C.-W. Chang, in Thermal Transport in Low Dimensions: From Statistical Physics to Nanoscale Heat Transfer (Ref. [4]), pp. 305–338.
  13. Thermal Transport in Low Dimensions: From Statistical Physics to Nanoscale Heat Transfer (Ref. [4]).
  14. E. Fermi, J. Pasta, and S. Ulam, Studies of nonlinear problems, I, Los Alamos Scientific Laboratory Report No. LA-1940 (Los Alamos Scientific Laboratory, Los Alamos, NM, 1955).
  15. The Fermi-Pasta-Ulam Problem, edited by G. Gallavotti, Lecture Notes in Physics Vol. 728 (Springer, Berlin, 2007).
  16. R. Peierls, Ann. Phys. (NY) 395, 1055 (1929).
  17. V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I: Wave Turbulence (Springer, Berlin, 2012).
  18. Y. Choi, Y. V. Lvov, and S. Nazarenko, Physica D 201, 121 (2005).
  19. S. Nazarenko, Wave Turbulence, Lecture Notes in Physics Vol. 825 (Springer, Berlin, 2011).
  20. G. L. Eyink and Y.-K. Shi, Physica D 241, 1487 (2012).
  21. S. Chibbaro, G. Dematteis, C. Josserand, and L. Rondoni, Phys. Rev. E 96, 021101(R) (2017).
  22. S. Chibbaro, G. Dematteis, and L. Rondoni, Physica D 362, 24 (2018).
  23. M. Onorato and G. Dematteis, J. Phys. Commun. 4, 095016 (2020).
  24. Y. V. Lvov and M. Onorato, Phys. Rev. Lett. 120, 144301 (2018).
  25. S. Lepri, R. Livi, and A. Politi, Europhys. Lett. 43, 271 (1998).
  26. A. Pereverzev, Phys. Rev. E 68, 056124 (2003).
  27. K. Aoki, J. Lukkarinen, and H. Spohn, J. Stat. Phys. 124, 1105 (2006).
  28. J. Lukkarinen and H. Spohn, Commun. Pure Appl. Math. 61, 1753 (2008).
  29. G. Dematteis, L. Rondoni, D. Proment, F. De Vita, and M. Onorato, Phys. Rev. Lett. 125, 024101 (2020).
  30. Y. Deng and Z. Hani, arXiv:2104.11204.
  31. I. Ampatzoglou, C. Collot, and P. Germain, arXiv:2107.11819.
  32. M. Rosenzweig and G. Staffilani, Physica D 433, 133148 (2022).
  33. M. D. Bustamante, K. Hutchinson, Y. V. Lvov, and M. Onorato, Commun. Nonlinear Sci. Numer. Simulat. 73, 437 (2019).
  34. S. Nazarenko, A. Soffer, and M.-B. Tran, Entropy 21, 823 (2019).
  35. J. Lukkarinen, in Thermal Transport in Low Dimensions: From Statistical Physics to Nanoscale Heat Transfer (Ref. [4]), pp. 159–214.
  36. H. Spohn, in Thermal Transport in Low Dimensions: From Statistical Physics to Nanoscale Heat Transfer (Ref. [4]), pp. 107–158.
  37. A. Mellet and S. Merino-Aceituno, J. Stat. Phys. 160, 583 (2015).
  38. V. P. Peshkov et al., Helium 4, 166 (2013).
  39. V. A. Kuzkin and A. M. Krivtsov, Phys. Rev. E 101, 042209 (2020).
  40. V. A. Kuzkin and A. M. Krivtsov, Acta Mech. 232, 1983 (2021).
  41. M. Chester, Phys. Rev. 131, 2013 (1963).
  42. E. Prohofsky and J. Krumhansl, Phys. Rev. 133, A1403 (1964).
  43. D. Chandrasekharaiah, ASME Appl. Mech. Rev. 39, 355 (1986).
  44. S. Huberman, R. A. Duncan, K. Chen, B. Song, V. Chiloyan, Z. Ding, A. A. Maznev, G. Chen, and K. A. Nelson, Science 364, 375 (2019).
  45. G. Chen, Nat. Rev. Phys. 3, 555 (2021).

Outline

Information

Phys. Rev. E 106, 034110– Published 7 September, 2022
  • Received 4 April 2022
  • Accepted 13 July 2022
Article part of CHORUS
Crossmark - Check for updates button

©2022 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation