The Fourier law in a momentum-conserving chain

Journal of Statistical Mechanics: Theory and Experiment

Volumn , Issue 5, 2005, Pages 143-161

  Giardinà, Cristian ^a   Kurchan, Jorge ^b  

^a EURANDOM   (Netherlands)

^b ESPCI   (France)

Author keywords

Transport processes heat transfer (theory)

Indexed keywords

EID: 21244479337     PISSN: 17425468     EISSN: None     Source Type: Journal    
DOI: 10.1088/1742-5468/2005/05/P05009     Document Type: Article

References (40)

1. Bonetto F, Lebowitz J and Rey-Bellet L 2000 Fourier's law: a challenge for theorists Mathematical Physics 2000 ed A Fokas, A Grigoryan, T Kibble and B Zegarlinsky (London: Imperial College) pp.128-50
2. Lepri S, Livi R and Politi A 2003 Thermal conduction in classical low dimensional lattices Phys. Rep. 377 1
3. Rieder Z, Lebowitz J L and Lieb E 1967 Properties of a harmonic crystal in a stationary nonequilibrium state J. Math. Phys. 8 1073
4. Nakazawa H 1970 On the lattice thermal conduction Suppl. Prog. Theor. Phys. 45 231
5. Lepri S, Livi R and Politi A 1997 Heat conduction in chains of nonlinear oscillators Phys. Rev. Lett. 78 1896
6. Hatano T 1999 Heat conduction in the diatomic Toda lattice revisited Phys. Rev. E 59 R1
7. Dhar A 2001 Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses Phys. Rev. Lett. 86 3554
8. Grassberger P, Nadler W and Yang L 2002 Heat conduction and entropy production in a one-dimensional hard-particle gas Phys. Rev. Lett. 89 180601
9. Casati G and Prosen T 2003 Anomalous heat conduction in a di-atomic one-dimensional ideal gas Phys. Rev. E 67 015203(R)
10. Deutsch J M and Narayan O 2003 One-dimensional heat conductivity exponent from a random collision model Phys. Rev. E 68 010201
11. Giardiná C, Livi R, Politi A and Vassalli M 2000 Finite thermal conductivity in 1D lattices Phys. Rev. Lett. 84 2144
12. Gendelman O V and Savin A V 2000 Normal heat conductivity of the one-dimensional lattice with periodic potential of nearest-neighbor interaction Phys. Rev. Lett. 84 2381
13. Casati G, Ford J, Vivaldi F and Visscher W 1984 One-dimensional classical many-body system having a normal thermal conductivity Phys. Rev. Lett. 53 1120
14. Prosen T and Robnik M 1992 Energy transport and detailed verification of Fourier heat law in a chain of colliding harmonic oscillators J. Phys. A: Math. Gen. 25 3449
15. Hu B, Li B and Zhao H 1998 Heat conduction in one-dimensional chains Phys. Rev. E 57 2992
16. Tsironis G P, Bishop A R, Savin A V and Zolotaryuk A V 1999 Dependence of thermal conductivity on discrete breathers in lattices Phys. Rev. E 60 6610
17. Bunimovich L and Sinai Ya G 1981 Commun. Math. Phys. 78 661
18. Lebowitz J L and Spohn H 1978 J. Stat. Phys. 19 633
19. Alonso D, Artuso R, Casati G and Guarneri I 1999 Heat conductivity and dynamical instability Phys. Rev. Lett. 82 1859
20. Mejá-Monasterio C, Larralde H and Leyvraz F 2001 Coupled normal heat and matter transport in a simple model system Phys. Rev. Lett. 86 5417
21. Alonso D, Ruiz A and de Vega I 2002 Polygonal billiards and transport: diffusion and heat conduction Phys. Rev. E 66 66131
22. Li B, Wang L and Hu B 2002 Finite thermal conductivity in 1D models having zero Lyapunov exponents Phys. Rev. Lett. 88 223901
23. Li B, Casati G and Wang J 2003 Heat conductivity in linear mixing systems Phys. Rev. E 67 21204
24. Casher A and Lebowitz J L 1971 J. Math. Phys. 12 1701
25. Rubin R J and Greer W L 1971 J. Math. Phys. 12 1686
26. O'Connor A J and Lebowitz J L 1974 J. Math. Phys. 15 692
27. Li B, Zhao H and Hu B 2001 Can disorder induce a finite thermal conductivity in 1D lattices? Phys. Rev. Lett. 86 63
28. Galves A, Kipnis C, Marchioro C and Presutti E 1981 Commun. Math. Phys. 81 127
29. Kipnis C, Marchioro C and Presutti E 1982 Heat flow in an exactly solvable model J. Stat. Phys. 27 65
30. Eckmann J P and Young L-S 2004 Temperature profiles in Hamiltonian heat conduction Europhys. Lett. 68 790
31. See also Mejia-Monasterio C, Larralde H and Leyvraz F 2001 Observation of coupled normal heat and matter transport in a simple model system Phys. Rev. Lett. 86 5417
32. Bertini L, Gabrielli D and Lebowitz J L 2005 Large deviations for a stochastic model of heat flow Preprint at press
33. Lepri S, Livi R and Politi A 1998 On the anomalous thermal conductivity in one dimensional lattices Europhys. Lett. 43 271
34. Narayan O and Ramaswamy S 2002 Anomalous heat conduction in one-dimensional momentum-conserving systems Phys. Rev. Lett. 89 200601
35. Wang J-S and Li B 2004 Mode-coupling theory and molecular dynamics simulation for heat conduction in a chain with transverse motions Phys. Rev. E 70 021204
36. Lippi A and Livi R 2000 Heat conduction in 2d nonlinear lattices J. Stat. Phys. 100 1147
37. Grassberger P and Yang L 2002 Heat conduction in low dimensions: from Fermi-Pasta-Ulam chains to single-walled nanotubes Preprint cond-mat/0204247
38. Yang L 2002 Finite heat conduction in a 2D disorder lattice Phys. Rev. Lett. 88 094301
39. Risken H 1996 The Fokker Planck Equation 2nd edn (Berlin: Springer)
40. Olla S 2005 at press