Dissipative dynamics of the Frenkel-Kontorova model

Advances in Physics

Volumn 45, Issue 6, 1996, Pages 505-598

  Floría, Luis M ^a   Mazo, Juan J ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MECHANICS; ELECTRON ENERGY LEVELS; JOSEPHSON JUNCTION DEVICES; MATHEMATICAL MODELS;

CHARGE DENSITY WAVE CONDUCTORS; FRENKEL-KONTOROVA MODEL;

ELECTRON TRANSITIONS;

EID: 0030288152     PISSN: 00018732     EISSN: 14606976     Source Type: Journal    
DOI: 10.1080/00018739600101557     Document Type: Article

References (133)

1. Yeomans, J. M., 1988, Solid State Physics Vol. 41, edited by H. Ehrenreich and D. Turnbull (New York: Academic).
2. Griffiths, R. B., 1990, Fundamental Problems in Statistical Mechanics VII, edited by H. van Beijeren (Amsterdam: North-Holland).
3. Aubry, S., 1992, Twist Mappings and their Applications, edited by R. McGehee and K. R. Meyer (New York: Springer-Verlag).
4. Aubry, S., and Abramovici, G., 1990, Physica D, 43, 199.
5. Aubry, S., Gosso, J. R, Abramovici, G., Raimbault J. L., and Quemerais, R, 1991, Physica D, 47, 461.
6. Aubry, S., Mackay, R. S., and Baesens, C., 1992, Physica D, 56, 123.
7. Baesens, C., and Mackay, R. S., 1993, Physica D, 69, 59.
8. Baesens, C, and Mackay, R. S., 1994, Nonlinearity, 7, 59.
9. Fisher, M. E., and Szpilka, A. M., 1987, Phys. Rev. B, 36, 644, 5343.
10. Harris, A. B., Micheletti, C., and Yeomans, J. M., 1995, Phys. Rev. Lett., 74, 3045.
11. Szpilka, A. M., and Fisher, M. E., 1986, Phys. Rev. Lett., 57, 1044.
12. Yeomans, J. M., 1995, OUTP-95-335.
13. Yeomans, J. M., private communication.
14. Selke, W., 1993, Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (New York: Academic).
15. Aubry, S., 1985, Structures et Instabilités, edited by C. Godréche (Les Ulis, France: Editions de Physique).
16. Braiman, Y, Baumgarten, J., Jortner, J., and Klafter, J., 1990, Phys. Rev. Lett., 65, 2398.
17. Meiss, J. D., 1992, Rev. mod. Phys., 64, 795.
18. Sasaki, K., and Griffiths, R. B., 1988, J. statist. Phys., 53, 1031.
19. Aubry, S., 1983, Physica D, 7, 240.
20. Coppersmith, S. N., and Fisher, D. S., 1983, Phys. Rev. B, 28, 2566.
21. Aubry, S., and Le Daeron, P. Y, 1983, Physica D, 8, 381.
22. Chou, W., and Griffiths, R. B., 1986, Phys. Rev. B, 34, 6219.
23. Griffiths, R. B., and Chou, W., 1986, Phys. Rev. Lett., 56, 1929.
24. Sasaki, K., and Floría, L. M., 1989, J. Phys: condens. Matter, 1, 2179.
25. Tang, L. H., and Griffiths, R. B., 1988, J. statist. Phys., 53, 853.
26. Sasaki, K., 1991, Physica A, 171, 80.
27. Tang, L. H., 1987, Ph.D. thesis, Camegie-Mellon University.
28. Szpilka, A. M., and Fisher, M. E., 1987, Phys. Rev. B, 36, 5363.
29. Yokoi, C. S. O., Tang, L. H., and Chou, W., 1988, Phys. Rev. B, 37, 2173.
30. Villain, J., 1985, Structures et Instabilités, edited by C. Godréche (Les Ulis, France: Editions de Physique).
31. Mackay, R. S., 1982. Ph.D. thesis, Princeton University. Reprinted version in: MacKay, R. S., 1993, Renormalisation in Area-preserving Maps (Singapore: World Scientic).
32. Peyrard, M., and Aubry, S., 1983, J. Phys. C, 16, 1593.
33. De Seze, L., and Aubry, S., 1984, J. Phys. C, 17, 389.
34. Aubry, S., and Quemerais, P., 1989, Low Dimensional Electronic Properties of Molybdenum Bronzes and Oxides, edited by C. Schlenker (Dordrecht: Kluwer).
35. Mackay, R. S., 1991, Physica D, 50, 71.
36. Kadanoff, L. P., 1981, Phys. Rev. Lett., 47, 1641.
37. Shenker, S. J., and Kadanoff, L. P., 1982, J. statist. Phys., 27, 631.
38. Coppersmith, S. N., 1987, Phys. Rev. A, 36, 3375.
39. Mackay, R. S., and Aubry, S., 1994, Nonlinearity, 7, 1623.
40. Aubry, S., Abramovici, G., and Raimbault, J. L., 1992, J. statist. Phys., 67, 675.
41. Marín, J. L., and Aubry, S., 1996, Nonlinearity (to be published). Dissipative dynamics of the Frenkel-Kontorova model
42. Prigodin, V. N., and Samukhin, A. N., 1989, Zh. Eksp. Teor. Fiz., 95, 642
43. Prigodin, V. N., and Samukhin, A. N., 1989, Sov. 597 Phys. JETP, 68, 362).
44. Burkov, S. E., 1991, Phys. Rev. B, 44, 2850.
45. Blatter, G., Feigel'Man, M. F., Geshkenbein, V. B., Larkin, A. I., and Vinokur, V. M., 1994, Rev. mod. Phys., 66, 1125.
46. Gorkov, L. P., and Grüner, G., (Editors), 1989, Charge Density Waves in Solids, Modem Problems in Condensed Matter Sciences, Vol. 25 (Amsterdam: North-Holi and).
47. Grüner, G., 1988, Rev. mod. Phys., 60, 1129.
48. Jerome, D., and Schulz, H. J., 1982, Adv. Phys., 31, 299.
49. Jerome, D., and Caron, L. G., (Editors). 1987, Low-dimensional Conductors and Super conductors, NATO ASI Series B, Vol. 155 (New York: Plenum).
50. Peierls, R. E., 1955, Quantum Theory of Solids (Oxford: Oxford University Press).
51. Fröhlich, H., 1954, Proc. R. Soc. A, 233, 296.
52. Fogle, W., and Perlstein, H., 1972, Phys. Rev., B, 6, 1402.
53. Monceau, P., Ong, N. P., Portis, A. M., Meerschaut, A., and Rouxel, J., 1976, Phys. Rev. Lett., 37, 6902.
54. Hall, R. P., Hundley, M. F., and Zettl, A., 1988, Phys. Rev. B, 38.
55. Fleming, R. M., and Grimes, C. C., 1979, Phys. Rev. Lett., 42, 1423.
56. Monceau, P., Richard, J., and Renard, M., 1980, Phys. Rev. Lett., 45, 43.
57. Grüner, G., Zawadowski, A., and Chaikin, P. M., 1981, Phys. Rev. Lett., 46, 511.
58. Monceau, P., Richard, J., and Renard, M., 1982, Phys. Rev. B, 25, 931.
59. Bardeen, J., 1979, Phys. Rev. Lett., 42, 1498.
60. Bardeen, J., 1980, Phys. Rev. Lett., 45, 1978.
61. Thorne, R. E., Hjcker, J. R., Bardeen, J., Brown, S. E., and Grüner, G., 1986, Phys. Rev. B, 33, 7342.
62. Fukuyama, H., and Lee, P. A., 1977, Phys. Rev. B, 17, 535.
63. Sneddon, L., Cross, M. C., and Fisher, D. S., 1982, Phys. Rev. Lett., 49, 292.
64. Fisher, D. S., 1985, Phys. Rev. B, 31, 1396.
65. Fisher, D. S., 1983, Phys. Rev. Lett., 50, 1486.
66. Sneddon, L., 1984, Phys. Rev. Lett., 52, 65.
67. Sneddon, L., 1984, Phys. Rev. B, 30, 2974.
68. Coppersmith, S. N., and Fisher, D. S., 1988, Phys. Rev. A, 38, 6338.
69. Middleton, A. A., and Fisher, D. S., 1993, Phys. Rev. B, 47, 3530.
70. Narayan, O., and Fisher, D. S., 1992, Phys. Rev. B, 46, 11 520.
71. Coppersmith, S. N., and Littlewood, P. B., 1987, Phys. Rev. B, 36, 311.
72. Littlewood, P. B., 1989, Charge Density Waves in Solids, edited by L. P. Gorkov and G. Grüner, Modem Problems in Condensed Matter Sciences, Vol. 25 (Amsterdam: North-Holland), p. 321.
73. Middleton, A. A., Biham, O., Littlewood, P. B., and Sibani, P., 1992, Phys. Rev. Lett., 68, 1586.
74. Middleton, A. A., 1990, Ph.D. thesis, Princeton University.
75. Middleton, A. A., and Fisher, D. S., 1991, Phys. Rev. Lett., 66, 92.
76. Middleton, A. A., 1992, Phys. Rev. Lett., 68, 670.
77. Inui, M., Hall, R. P., Doniach, S., and Zettl, A., 1988, Phys. Rev. B, 38, 13 047.
78. Levy, J., Sherwin, M. S., Abraham, F. F., and Wiesenfeld, K., 1992, Phys. Rev. Lett., 68, 2968.
79. Josephson, B. D., 1962, Phys. Lett., 1, 251.
80. Josephson, B. D., 1964, Rev. mod. Phys., 36, 216.
81. Josephson, B. D., 1965, Adv. Phys., 14, 419.
82. Anderson, P. W., and Rowell, J. M., 1963, Phys. Rev. Lett., 10, 230.
83. Shapiro, S., 1963, Phys. Rev. Lett., 11, 80.
84. Barone, A., and Paterno, G., 1982, Physics and Applications of the Josephson Effect (New York: Wiley).
85. Lindelof, P. E., 1981, Rep. Progr. Phys., 44, 949.
86. Woldram, J. R., 1976, Rep. Progr. Phys., 39, 751.
87. Stewart, W. C., 1968, Appl. Phys. Lett., 12, 277.
88. Mccumber, D. E., 1968, J. appl. Phys., 39, 2503.
89. Mccumber, D. E., 1968, J. appl. Phys., 39, 3113.
90. Ustinova, V., Cirillo, M-, and Malomed, B. A., 1993, Phys. Rev. B, 47, 8357.
91. Ustinov, A. V., Cirillo, M., Larsen, B. H., Oboznov, V. A., Carelli, P., and Rotoli, G., 1995, Phys. Rev. B, 51, 3081.
92. Van Der Zant, H. S. J., Orlando, T. P., Watanabe, S., and Strogatz, S. H., 1995, Phys. Rev. Lett., 74, 174.
93. Watanabe, S., Strogatz, S. H., Van Der Zant, H. S. J., and Orlando, T. P., 1995, Phys. Rev. Lett., 74, 379.
94. Yu, S., Kivshar, 1996, Phys. Rep. (to be published).
95. Kosterlitz, J. M., and Thouless, D. J., 1978, Progress in Low Temperature Physics, Vol. VIIB, edited by D. F. Brewer (Amsterdam: North-Holland).
96. Abraham, D. W., Lobb, C. J., Tïnkham, M., and Klapwijk, T. M., 1982, Phys. Rev. B, 26, 5268.
97. Lobb, C. J., Abraham, D. W., and Tïnkham, M., 1983, Phys. Rev. B, 27, 150.
98. Resnick, D. J., Garland, J. C., Boyd, J. T., Shoemaker, S., and Newrock, R. S., 1981, Phys. Rev. Lett., 47, 1542.
99. Voss, R. F., and Webb, R. A., 1982, Phys. Rev. B, 25, 3446.
100. Téitel, S., and Jayaprakash, C., 1983, Phys. Rev. Lett., 51, 1999.
101. Halsey, T. C., 1985, Phys. Rev. B, 31, 5728.
102. Straley, J. P., and Barnett, G. M., 1993, Phys. Rev. B, 48, 3309.
103. Chung, J. S., Lee, K. H., and Stroud, D., 1989, Phys. Rev. B, 40, 6570.
104. Falo, F., Bishop, A. R., and Lomdahl, P. S., 1990, Phys. Rev. B, 41, 10983.
105. Mon, K. K., and Tieitel, S., 1989, Phys. Rev. Lett., 62, 673.
106. Shenoy, S. R., 1985, J. Phys. C, 18, 5163.
107. Domínguez, D., and José, J. V., 1994, Int. J. mod. Phys. B, 8, 3749.
108. Kardar, M., 1986, Phys. Rev. B, 33, 3125.
109. Mazo, J. J., Falo, F., and Floría, L. M., 1995, Phys. Rev. B, 52, 10433.
110. Ciria, J. C., and Giovannella, C., 1995, Macroscopic Quantum Phenomena and Coherence in Superconducting Networks, edited by M. Tinkham and C. Giovannella (Singapore: World Scientific).
111. Kim, J., Choe, W. G., Kim, S., and Lee, H. J., 1994, Phys. Rev. B, 49, 459.
112. Kim, J. M., and Lee, S. J., 1994, Phys. Rev. B, 50.
113. Kim, B. J., Kim, S., and Lee, S. J., 1995, Phys. Rev. B, 51, 8462.
114. Yu, W., Harris, E. B., Hebboul, S. E., Garland, J. C., and Stroud, D., 1992, Phys. Rev. B, 45, 12624.
115. Angenent, S. B., 1988, Commun, math. Phys., 115, 353.
116. Hirsch, M., 1982, SIAM J. math. Anal., 13, 167.
117. Matano, H., 1982, J. Fac. Sci. Univ. Tokyo, 29, 401.
118. Natterman, T., Stepanow, S., Tang, L. H., and Leschhorn, H., 1992, J. Physique II, 2, 1483.
119. Barabási, A. L., and Stanley, H. E., 1995, Fractal concepts in Surface Growth (Cambridge: Cambridge University Press).
120. Bergé, F., Pomeau, Y, and Vidal, Ch., 1984, Order Within Chaos (New York: Wiley).
121. Pomeau, Y, and Manneville, P., 1980, Commun, math. Phys., 74, 189.
122. Aubry, S., 1983, J. Phys. C, 16, 2497.
123. Coppersmith, S. N., and Littlewood, P. B., 1986, Phys. Rev. Lett., 57, 1927.
124. Tang, C., Wiesenfeld, K., Bak, P., Coppersmith, S. N., and Littlewood, P. B., 1987, Phys. Rev. Lett., 58, 1161.
125. Waldram, J. R., Pippard, A. B., and Clarke, J., 1968, Phil. Trans. R. Soc. Lond. A, 268, 265.
126. Hamilton, C. A., and Johnson, E. G., 1972, Phys. Lett. A, 41, 393.
127. Russer, P., 1972, J. appl. Phys., 43, 2008.
128. Renné, M. J. and Polder, D., 1974, Rev. Phys. Appl., 9, 25.
129. Waldram, J. R., and Wu, P. H., 1982, J. low temp. Phys., 47, 363.
130. Inui, M., and Doniach, S., 1987, Phys. Rev. B, 35, 6244.
131. Falo, F., Floría, L. M., Martínez, P. J., and Mazo, J. J., 1993, Phys. Rev. B, 48, 7434.
132. Floría, L. M. and Falo, F., 1992, Phys. Rev. Lett., 68, 2713.
133. Mazo, J. J., Falo, F., and Floría, L. M., 1995, Phys. Rev. B, 52, 6451.