Skip to main content
SpringerLink
Log in

Heat Conduction in Two-Dimensional Nonlinear Lattices

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The divergence of the heat conductivity in the thermodynamic limit is investigated in 2d-lattice models of anharmonic solids with nearest-neighbour interaction from single-well potentials. Two different numerical approaches based on nonequilibrium and equilibrium simulations provide consistent indications in favour of a logarithmic divergence in “ergodic”, i.e., highly chaotic, dynamical regimes. Analytical estimates obtained in the framework of linear-response theory confirm this finding, while tracing back the physical origin of this anomalous transport to the slow diffusion of the energy of hydrodynamic modes. Finally, numerical evidence of superanomalous transport is given in the weakly chaotic regime, typically observed below a threshold value of the energy density.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. R. E. Peierls, Quantum Theory of Solids (Oxford University Press, London, 1955).

    Google Scholar 

  2. Z. Rieder, J. L. Lebowitz, and E. Lieb, J. Math. Phys. 8:1073 (1967).

    Google Scholar 

  3. F. Mokross and H. Bü ttner, J. Phys. C 16:4539 (1983).

    Google Scholar 

  4. K. Ishii and H. Matsuda, Prog. Theor. Phys. Suppl. 45:56 (1970).

    Google Scholar 

  5. J. B. Keller, G. C. Papanicolaou, and J. Weilenmann, Comm. Pure and App. Math. 32:583 (1978).

    Google Scholar 

  6. A. Casher and J. L. Lebowitz, J. Math. Phys. 12:1701 (1971); A. J. O'Connor and J. L. Lebowitz, J. Math. Phys. 15:692 (1974).

    Google Scholar 

  7. N. Nakazawa, Progr. Theor. Phys. Suppl. 45:231 (1970).

    Google Scholar 

  8. D. N. Payton, M. Rich, and W. M. Visscher, Phys. Rev. 160:706 (1967).

    Google Scholar 

  9. W. M. Visscher, Methods in Computational Physics (Academic Press, New York, 1976).

    Google Scholar 

  10. G. Casati, J. Ford, F. Vivaldi, and W. M. Visscher, Phys. Rev. Lett. 52:1861 (1984).

    Google Scholar 

  11. T. Prosen and M. Robnick, J. Phys. A 25:3449 (1992).

    Google Scholar 

  12. E. A. Jackson and A. D. Mistriotis, J. Phys. Condens. Matter 1:1223 (1989).

    Google Scholar 

  13. H. Kaburaki and M. Machida, Phys. Lett. A 181:85 (1993).

    Google Scholar 

  14. B. Hu, B.-W. Li, and H. Zhao, Phys. Rev. E 57:2992 (1998).

    Google Scholar 

  15. C. Alabiso, M. Casartelli, and P. Marenzoni, J. Stat. Phys. 79:451 (1995).

    Google Scholar 

  16. S. Lepri, R. Livi, and A. Politi, Europhys. Lett. 43:271 (1998).

    Google Scholar 

  17. S. Lepri, R. Livi, and A. Politi, Phys. Rev. Lett. 78:1896 (1997).

    Google Scholar 

  18. Y. Pomeau and R. Ré sibois, Phys. Rep. 19:63 (1975).

    Google Scholar 

  19. M. H. Ernst, Physica D 47:198 (1991).

    Google Scholar 

  20. T. Hatano, Phys. Rev. E 59:R1 (1999).

    Google Scholar 

  21. M. Vassalli, Diploma Thesis (University of Florence, 1998).

  22. A. Lippi, Diploma Thesis (University of Florence, 1999).

  23. C. Giardiná, R. Livi, A. Politi, and M. Vassalli, Phys. Rev. Lett. 84:2144 (2000).

    Google Scholar 

  24. G. Benettin and A. Tenenbaum, Phys. Rev. A 28:3020 (1983).

    Google Scholar 

  25. L. Casetti, R. Livi, A. Macchi, and M. Pettini, Europhys. Lett. 32:549 (1995).

    Google Scholar 

  26. C. Giardinà and R. Livi, J. Stat. Phys. 91:1027 (1998).

    Google Scholar 

  27. R. D. Mountain and R. A. MacDonald, Phys. Rev. B 28:3022 (1983).

    Google Scholar 

  28. N. Nishiguchi, Y. Kawada, and T. Sakuma, J. Phys.: Condens. Matter 4:10227 (1992).

    Google Scholar 

  29. S. Lepri, R. Livi, and A. Politi, Physica D 119:140 (1998).

    Google Scholar 

  30. S. Nosé, J. Chem. Phys. 81:511 (1984).

    Google Scholar 

  31. W. G. Hoover, Phys. Rev. A 31:1695 (1985).

    Google Scholar 

  32. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II, Springer Series in Solid State Sciences, Vol. 31 (Springer, Berlin, 1991).

    Google Scholar 

  33. B. Alder and T. Wainwright, Phys. Rev. Lett. 18:968 (1967).

    Google Scholar 

  34. J. P. Boon and S. Yip, Molecular Hydrodynamics (McGrawHill, New York, 1980).

    Google Scholar 

  35. R. I. Maclachlan and P. Atela, Nonlinearity 5:541 (1992).

    Google Scholar 

  36. S. Lepri, Phys. Rev. E 58:7165 (1998).

    Google Scholar 

  37. E. Fermi, J. Pasta, and S. Ulam, Los Alamos report LA-1940 (1955); reprinted in E. Fermi, Collected Papers, Vol. II (University of Chicago Press, Chicago, 1965), p. 978.

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica dell'Università, L.go E.Fermi 2, I-50125, Firenze, Italy

    Andrea Lippi & Roberto Livi

  2. Istituto Nazionale di Fisica della Materia, Unità di Firenze, Italy

    Andrea Lippi

  3. Istituto Nazionale di Fisica della Materia, Unità di Firenze, Italy

    Roberto Livi

  4. Sezione di Firenze, Istituto Nazionale di Fisica Nucleare, Italy

    Roberto Livi

Authors
  1. Andrea Lippi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberto Livi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lippi, A., Livi, R. Heat Conduction in Two-Dimensional Nonlinear Lattices. Journal of Statistical Physics 100, 1147–1172 (2000). https://doi.org/10.1023/A:1018721525900

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018721525900

Search

Navigation