Abstract
The energy transport in one-dimensional nonlinear systems is discussed. By numerically studying a model system, we verify the Fourier heat law on purely dynamical grounds and we compute the coefficient of thermal conductivity K. The same value ofK is independently obtained by use of the Green-Kubo formalism.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. E. Peierls,Ann. Phys. (Leipzig) 5, 1055 (1929);Quantum Theory of Solids (Oxford University Press, Oxford, 1956).
P. G. Bergmann and J. L. Lebowitz,Phys. Rev. 99, 578 (1965); J. L. Lebowitz,Phys. Rev. 114, 1192 (1959); Z. Rieder, J. L. Lebowitz, and E. Lieb,J. Math. Phys. 8, 1073 (1967); A. Casher and J. L. Lebowitz,J. Math. Phys. 12, 1701 (1971).
R. H. G. Hellemann, “Heat Transport in Harmonic and Anharmonic Lattices,” thesis, Yeshiva University (1971).
N. Nakazawa,Prog. Theor. Phys. Suppl. 45, 231 (1970); K. R. Allen and J. Ford,Phys. Rev. 187, 1132 (1969).
G. Casati,Nuovo Cimento B 52, 257 (1979); I. Guarneri,Boll. Unione Mat. Ital. 17B, 1034 (1980).
J. Ford, unpublished.
A. Casher and J. L. Lebowitz,J. Math. Phys. 12, 1701 (1971).
H. Matsuda and K. Ishii,Prog. Theor. Phys. Suppl. 45, 56 (1970); K. Ishii,Prog. Theor. Phys. Suppl. 53, 77 (1973).
D. N. Payton, M. Rich, and W. M. Visscher,Phys. Rev. 160, 706 (1967).
V. M. Visscher,Prog. Theor. Phys. 46, 729 (1971).
A. J. O'Connor and J. L. Lebowitz,J. Math. Phys. 15, 692 (1974).
R. J. Bell,Rep. Prog. Phys. 35, 1315 (1972).
J. L. Lebowitz and H. Spohn, “Transport Properties of the Lorentz Gas: Fourier's Law,” preprint; E. B. Davies, “A Model of Heat Conduction,” preprint (1977).
W. M. Visscher, inMethods in Computational Physics, Vol. 15 (Academic Press, New York, 1976) pp. 371–408.
E. A. Jackson, J. R. Pasta, and J. F. Waters,J. Comput Phys. 2, 207 (1968).
K. Miura, Ph.D. Thesis, University of Illinois, Urbana (1973).
D. N. Payton, M. Rich, and W. M. Visscher, inLocalized Excitations in Solids, R. F. Wallis, ed. (Plenum, New York, 1968), pp. 657–664; M. Rich, W. M. Visscher, and D. N. Payton,Phys. Rev. A 4, 1682 (1971).
S. A. Rice, private communication.
G. Casati, J. Ford, W. M. Visscher, and F. Vivaldi,Phys. Rev. Lett. 52, 1861 (1984).
G. Casati, J. Ford, W. M. Visscher, and F. Vivaldi: “Energy Propagation in One-Dimensional System: Validity of Fourier Law,” preprint.
G. Casati and J. Ford,J. Comput. Phys. 20, 97 (1976).
A. Hobson,J. Math. Phys. 16, 2210 (1975).
R. Aizemann, S. Goldstein, and J. Lebowitz,Commun. Math. Phys. 39, 289 (1975).
W. M. Visscher,Phys. Rev. A 10, 2461 (1974).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Casati, G. Energy transport and the Fourier heat law in classical systems. Found Phys 16, 51–61 (1986). https://doi.org/10.1007/BF00735180
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00735180