Thermal conduction in classical low-dimensional lattices

Physics Reports

Volumn 377, Issue 1, 2003, Pages 1-80

  Lepri, Stefano ^a,b   Livi, Roberto ^b,c   Politi, Antonio ^b,d  

^a Dipartimento di Energetica   (Italy)

^b Istituto Nazionale di Fisica   (Italy)

^c Dipartimento di Fisica   (Italy)

^d ISTITUTO NAZIONALE DI OTTICA   (Italy)

Author keywords

Classical lattices; Thermal conductivity

Indexed keywords

EID: 0037375035     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(02)00558-6     Document Type: Review

References (128)

1. S.R. de Groot, P. Mazur, Non-Equilibrium Thermodynamics, Dover, New York, 1984.
2. R.E. Peierls, Quantum Theory of Solids, Oxford University Press, London, 1955.
3. F. Bonetto, J. Lebowitz, L. Rey-Bellet, in: A. Fokas, A. Grigoryan, T. Kibble, B. Zegarlinski (Eds.), Mathematical Physics 2000, Imperial College, London, 2000.
4. J. Maddox, Nature 309 (7) (1984) 511
5. F. Mokross, H. Büttner, ibid. 5983 (1984) 217.
6. Y. Pomeau, R. Résibois, Phys. Rep. 19 (1975) 63.
7. D.T. Morelli, J. Heremans, M. Sakamoto, C. Uher, Phys. Rev. Lett. 57 (1986) 869.
8. A. Smontara, J.C. Lasjaunas, R. Maynard, Phys. Rev. Lett. 77 (1996) 5397.
9. A.V. Sologubenko, et al., Phys. Rev. B 64 (2001) 054412.
10. H. Forsman, P. Anderson, J. Chem. Phys. 80 (1984) 2804.
11. T.S. Tighe, J.M, Worlock, M.L. Roukes, Appl. Phys. Lett. 70 (1997) 2687.
12. M.M. Leivo, J.P. Pekola, Appl. Phys. Lett. 72 (1998) 1305.
13. W. Holmes, et al., Appl. Phys. Lett. 72 (1998) 2250.
14. J. Hone, et al., Phys. Rev. B 59 (1999) R2514.
15. P. Kim, L. Shi, A. Majumdar, P.L. McEuen, Phys. Rev. Lett. 87 (2001) 215 502.
16. L.G.C. Rego, G. Kirczenow, Phys. Rev. Lett. 81 (1998) 232.
17. D.M. Leitner, P.G. Wolynes, Phys. Rev. E 61 (2000) 2902.
18. K. Saito, S. Takesue, S. Miyashita, Phys. Rev. E 61 (2000) 2397, ibid. 54 (1996) 2404, J. Phys. Soc. Japan 65 (1996) 1243.
19. E. Fermi, J. Pasta, S. Ulam, in: E. Fermi (Ed.), Collected Papers, Vol. 2, University of Chicago Press, Chicago, Vol. 2, 1965, p. 78.
20. H.H. Rugh, Phys. Rev. Lett. 78 (1997) 772.
21. C. Giardinà, R. Livi, J. Stat. Phys. 91 (1998) 1027.
22. J. Lebowitz, J.K. Percus, L. Verlet, Phys. Rev. 153 (1967) 250.
23. A.I. Khinchin, Mathematical Foundations of Statistical Mechanics, Dover, New York, 1949.
24. Ph. Choquard, Helv. Phys. Acta 36 (1963) 415.
25. R.J. Hardy, Phys. Rev. 132 (1963) 168.
26. R. Kubo, M. Toda, N. Hashitsume, Statistical Physics II, in: Springer Series in Solid State Sciences, Vol. 31, Springer, Berlin, 1991.
27. R.A. MacDonald, D.H. Tsai, Phys. Rep. 46 (1978) 1.
28. A. Casher, J.L. Lebowitz, J. Math. Phys. 12 (1971) 1701.
29. R.J. Rubin, W.L. Greer, J. Math. Phys. 12 (1971) 1686.
30. A.J. O'Connor, J.L. Lebowitz, J. Math. Phys. 15 (1974) 692.
31. H. Spohn, J.L. Lebowitz, Commun. Math. Phys. 54 (1977) 97.
32. J.-P. Eckmann, C.-A. Pillet, L. Rey-Bellet, Commun. Math. Phys. 201 (1999) 657.
33. D.N. Payton, M. Rich, W.M. Visscher, Phys. Rev. 160 (1967) 706.
34. R.I. Mclachlan, P. Atela, Nonlinearity 5 (1992) 541.
35. L. Casetti, Phys. Scr. 51 (1995) 29.
36. R. Tehver, F. Toigo, J. Koplik, J.R. Banavar, Phys. Rev. E 57 (1998) R17.
37. D.J. Evans, G.P. Morriss, Statistical Mechanics of Nonequilibrium Liquids, Academic Press, San Diego, 1990.
38. S. Nosé, J. Chem. Phys. 81 (1984) 511.
39. W.G. Hoover, Phys. Rev. A 31 (1985) 1695.
40. Focus issue on "Chaos and irreversibility" CHAOS 8 (2) (1998).
41. N. Chernov, J.L. Lebowitz, J. Stat. Phys. 86 (1997) 953.
42. H. van Beijeren, private communication.
43. M.J. Gillan, R.W. Holloway, J. Phys. C 18 (1985) 5705.
44. A. Maeda, T. Munakata, Phys. Rev. E 52 (1995) 234.
45. F. Zhang, D.J. Isbister, D.J. Evans, Phys. Rev. E 61 (2000) 3541.
46. A. Filippov, B. Hu, B. Li, A. Zelser, J. Phys. A 31 (1998) 7719.
47. F.D. Di Tolla, M. Ronchetti, Phys. Rev. E 48 (1993) 1726.
48. M.E. Lumpkin, W.M. Saslow, W.M. Visscher, Phys. Rev. B 17 (1978) 4295.
49. E.L. Lifshitz, L.P. Pitaevskij, Physical Kinetics, Pergamon Press, New York, 1981.
50. K. Aoki, D. Kusnezov, Phys. Lett. A 265 (2000) 250.
51. K. Aoki, D. Kusnezov, Phys. Rev. Lett. 86 (2001) 4029.
52. Z. Rieder, J.L. Lebowitz, E. Lieb, J. Math. Phys. 8 (1967) 1073.
53. M.C. Wang, G.E. Uhlenbeck, Rev. Mod. Phys. 17 (1945) 323.
54. M. Bolsterli, M. Rich, W.M. Visscher, Phys. Rev. A 1 (1970) 1086.
55. B. Derrida, E. Garner, J. Phys. (Paris) 45 (1984) 1283.
56. H. Matsuda, K. Ishii, Suppl. Prog. Theor. Phys. 45 (1970) 56.
57. W.M. Visscher, Prog. Theor. Phys. 46 (1971) 729.
58. W. Frizzera, A. Monteil, A. Capobianco, Il Nuovo Cimento D 20 (1998) 1715.
59. J.B. Keller, G.C. Papanicolaou, J. Weilenmann, Comm. Pure App. Math. Vol. XXXII (1978) 583.
60. A. Dhar, Phys. Rev. Lett. 86 (2001) 5882.
61. E.A. Jackson, Rocky Mount. J. Math. 8 (1978) 127.
62. J. Callaway, Quantum Theory of the Solid State, Academic Press, San Diego, 1991.
63. S. Lepri, Eur. Phys. J. B 18 (2000) 441.
64. T. Prosen, D.K. Campbell, Phys. Rev. Lett. 84 (2000) 2857.
65. M.S. Green, Phys. Rev. 119 (1960) 829.
66. C. Alabiso, M. Casartelli, P. Marenzoni, J. Stat. Phys. 79 (1995) 451.
67. M.H. Ernst, Physica D 47 (1991) 198.
68. S. Lepri, Phys. Rev. E 58 (1998) 7165.
69. A. Lippi, R. Livi, J. Stat. Phys. 100 (2000) 1147.
70. D. D'Humieres, P. Lallemand, Y. Qian, C. R. Acad. Sci. Paris Ser. II 308 (1989) 585.
71. T. Naitoh, M.H. Ernst, M.A. van der Hoef, D. Frenkel, Phys. Rev. E 47 (1993) 4098.
72. S. Lepri, R. Livi, A. Politi, Europhys. Lett. 43 (1998) 271.
73. E.A. Jackson, J.R. Pasta, J.F. Waters, J. Comput. Phys. 2 (1968) 207.
74. N. Nakazawa, Progr. Theoret. Phys. 45 (Suppl.) (1970) 231.
75. W.M. Visscher, in: Methods in Computational Physics, Vol. 15, Academic Press, New York, 1976, p. 371.
76. H. Kaburaki, M. Machida, Phys. Lett. A 181 (1993) 85.
77. Y. Ohtsubo, N. Nishiguchi, T. Sakuma, J. Phys.: Condens. Matter 6 (1994) 3013.
78. F. Mokross, H. Büttner, J. Phys. C 16 (1983) 4539.
79. E.A. Jackson, A.D. Mistriotis, J. Phys.: Condens. Matter 1 (1989) 1223.
80. N. Nishiguchi, T. Sakuma, J. Phys.: Condens. Matter 2 (1990) 7575.
81. O.V. Gendelman, L.I. Manevich, Sov. Phys. JETP 75 (1992) 271.
82. M. Mareschal, A. Amellal, Phys. Rev. A 37 (1988) 2189.
83. S. Lepri, R. Livi, A. Politi, Phys. Rev. Lett. 78 (1997) 1896.
84. S. Lepri, R. Livi, A. Politi, Physica D 119 (1998) 140.
85. T. Hatano, Phys. Rev. E 59 (1999) R1.
86. M. Vassalli, Diploma Thesis, University of Florence, 1999.
87. W. Frizzera, G. Viliani, M. Montagna, A. Monteil, A. Capobianco, J. Phys.: Condens. Matter 9 (1997) 10 867.
88. G. Casati, Found. Phys. 16 (1986) 51.
89. A. Dhar, Phys. Rev. Lett. 86 (2001) 3554.
90. P.L. Garrido, P.I. Hurtado, B. Nadrowski, Phys. Rev. Lett. 86 (2001) 5486.
91. Y. Du, H. Li, L.P. Kadanoff, Phys. Rev. Lett. 74 (1995) 1268.
92. G. Casati, T. Prosen, private communication.
93. C. Giardiná, R. Livi, A. Politi, M. Vassalli, Phys. Rev. Lett. 84 (2000) 2144.
94. O.V. Gendelman, A.V. Savin, Phys. Rev. Lett. 84 (2000) 2381.
95. G. Benettin, L. Galgani, A. Giorgilli, Il Nuovo Cimento B 89 (1985) 89.
96. R. Livi, M. Pettini, S. Ruffo, A. Vulpiani, J. Stat. Phys. 48 (1987) 539.
97. D. Escande, H. Kantz, R. Livi, S. Ruffo, J. Stat. Phys. 76 (1994) 605.
98. M. Vassalli, unpublished.
99. J. Dawson, Phys. Fluids 5 (1962) 445.
100. G. Casati, J. Ford, F. Vivaldi, W.M. Visscher, Phys. Rev. Lett. 52 (1984) 1861.
101. D.J.R. Mimnagh, L.E. Ballentine, Phys. Rev. E 56 (1997) 5332.
102. M. Pettini, M. Cerruti-Sola, Phys. Rev. A 44 (1992) 975.
103. T. Prosen, M. Robnik, J. Phys. A 25 (1992) 3449.
104. H.A. Posch, W.G. Hoover, Phys. Rev. E 58 (1998) 4344.
105. C. Kipnis, C. Marchioro, E. Presutti, J. Stat. Phys. 27 (1982) 65.
106. B. Hu, B. Li, H. Zhao, Phys. Rev. E 57 (1998) 2992.
107. B. Hu, B. Li, H. Zhao, Phys. Rev. E 61 (1999) 3828.
108. G.P. Tsironis, A.R. Bishop, A.V. Savin, A.V. Zolotaryuk, Phys. Rev. E 60 (1999) 6610.
109. M. Toda, Phys. Scr. 20 (1979) 424.
110. P. Mazur, Physica 43 (1969) 533.
111. X. Zotos, J. Low Temp. Phys. 126 (3-4) (2002) 1185.
112. M. Toda, Theory of Non-linear Lattices, in: Springer Series in Solid-State Sciences, Vol. 20, Springer, Berlin, 1981.
113. M. Rich, W.M. Visscher, D.N. Payton, Phys. Rev. A 4 (1971) 1682.
114. R.D. Mountain, R.A. MacDonald, Phys. Rev. B 28 (1983) 3022.
115. T. Sakuma, Y. Ohtsubo, N. Nishiguchi, J. Phys.: Condens. Matter 4 (1992) 10 227.
116. J. Michalski, Phys. Rev. B 45 (1992) 7054.
117. R.H.H. Poetzsch, H. Böttger, Phys. Rev. B 50 (1994) 15 757.
118. R.H.H. Poetzsch, H. Böttger, J. Phys.: Condens. Matter 10 (1998) 943.
119. Ch. Dellago, H.A. Posch, Physica A 237 (1997) 95.
120. T. Shimada, T. Murakami, S. Yukawa, K. Saito, N. Ito, J. Phys. Soc. Japan 10 (2000) 3150.
121. G. Benettin, A. Tenenbaum, Phys. Rev. A 28 (1983) 3020.
122. A. Carati, L. Galgani, J. Stat. Phys. 94 (1999) 859.
123. S. Lepri, S. Ruffo, Europhys. Lett. 55 (2001) 512.
124. B. Li, H. Zhao, B. Hu, Phys. Rev. Lett. 86 (2001) 63.
125. E. Maciá, Phys. Rev. B 61 (2000) 6645.
126. P.B. Allen, J.L. Feldman, Phys. Rev. B 48 (1993) 12 581.
127. O. Narayan, S. Ramaswamy, Phys. Rev. Lett. 89 (2002) 200601.
128. P. Grassberger, et al., Phys. Rev. Lett. 89 (2002) 180601.