Velocity-force characteristics of an interface driven through a periodic potential

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 11, 2003, Pages 1154121-11541219

  Ettouhami, A M ^a   Radzihovsky, Leo ^a,b  

^a UNIVERSITY OF COLORADO   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; CRYSTALLIZATION; DYNAMICS; ENERGY; FORCE; MODEL; MOTION; TEMPERATURE; THEORY; VELOCITY;

EID: 0038556692     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (103)

1. J. Krim and G. Palasantzas, Int. J. Mod. Phys. B 9, 599 (1995).
2. M. Kardar, lectures given at the the Fourth CTP Workshop on Statistical Physics, Seoul National University, Korea; cond-mat/9704172 (unpublished).
3. G. Grüner, Rev. Mod. Phys. 60, 1129 (1988).
4. G. Blatter, M.V. Feigelman, V.B. Geshkenbein, A.I. Larkin, and V.M. Vinokur, Rev. Mod. Phys. 66, 1125 (1994).
5. T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 76, 3408 (1996); Phys. Rev. B 57, 11 356 (1998).
6. T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 76, 3408 (1996); Phys. Rev. B 57, 11 356 (1998).
7. L. Balents, M.C. Marchetti, and L. Radzihovsky, Phys. Rev. Lett. 78, 751 (1997); Phys. Rev. B 57, 7705 (1998).
8. L. Balents, M.C. Marchetti, and L. Radzihovsky, Phys. Rev. Lett. 78, 751 (1997); Phys. Rev. B 57, 7705 (1998).
9. S. Scheidl and V.M. Vinokur, Phys. Rev. B 57, 13 800 (1998).
10. E.A. Andrei, G. Deville, D.C. Glattli, F.I.B. Williams, E. Paris, and B. Etienne, Phys. Rev. Lett. 60, 2765 (1988).
11. D.S. Fisher, K. Dahmen, S. Ramanathan, and Y. Ben-Zion, Phys. Rev. Lett. 78, 4885 (1997)
12. M. O. Robbins and M. H. Müser, in Handbook of Modern Tribology, edited by Bharat Bhushan (CRC Press, Boca Raton, 2000).
13. K. Binder and A.P. Young, Rev. Mod. Phys. 58, 801 (1986).
14. J.G. Bednorz and K.A. Muller, Z. Phys. 64, 189 (1986).
15. D.S. Fisher, M.P.A. Fisher, and D.A. Huse, Phys. Rev. B 43, 130 (1991).
16. D.S. Fisher, Phys. Rev. Lett. 56, 1964 (1986).
17. T. Nattermann, Phys. Rev. Lett. 64, 2454 (1990); S.E. Korshunov, Phys. Rev. B 48, 3969 (1993); T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 72, 1530 (1994); Phys. Rev. B 52, 1242 (1995); T. Emig, S. Bogner, and T. Nattermann, Phys. Rev. Lett. 83, 400 (1999).
18. T. Nattermann, Phys. Rev. Lett. 64, 2454 (1990); S.E. Korshunov, Phys. Rev. B 48, 3969 (1993); T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 72, 1530 (1994); Phys. Rev. B 52, 1242 (1995); T. Emig, S. Bogner, and T. Nattermann, Phys. Rev. Lett. 83, 400 (1999).
19. T. Nattermann, Phys. Rev. Lett. 64, 2454 (1990); S.E. Korshunov, Phys. Rev. B 48, 3969 (1993); T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 72, 1530 (1994); Phys. Rev. B 52, 1242 (1995); T. Emig, S. Bogner, and T. Nattermann, Phys. Rev. Lett. 83, 400 (1999).
20. T. Nattermann, Phys. Rev. Lett. 64, 2454 (1990); S.E. Korshunov, Phys. Rev. B 48, 3969 (1993); T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 72, 1530 (1994); Phys. Rev. B 52, 1242 (1995); T. Emig, S. Bogner, and T. Nattermann, Phys. Rev. Lett. 83, 400 (1999).
21. T. Nattermann, Phys. Rev. Lett. 64, 2454 (1990); S.E. Korshunov, Phys. Rev. B 48, 3969 (1993); T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 72, 1530 (1994); Phys. Rev. B 52, 1242 (1995); T. Emig, S. Bogner, and T. Nattermann, Phys. Rev. Lett. 83, 400 (1999).
22. T. Nattermann and S. Scheidl, Adv. Phys. 49, 607 (2000).
23. L. Balents and D.S. Fisher, Phys. Rev. B 48, 5949 (1993).
24. L. Radzihovsky and J. Toner, Phys. Rev. Lett. 81, 3711 (1998).
25. S. Bhattacharya and M.J. Higgins, Phys. Rev. Lett. 70, 2617 (1993); Phys. Rev. B 52, 64 (1995); M.J. Higgins and S. Bhattacharya, Physica C 257, 232 (1996).
26. S. Bhattacharya and M.J. Higgins, Phys. Rev. Lett. 70, 2617 (1993); Phys. Rev. B 52, 64 (1995); M.J. Higgins and S. Bhattacharya, Physica C 257, 232 (1996).
27. S. Bhattacharya and M.J. Higgins, Phys. Rev. Lett. 70, 2617 (1993); Phys. Rev. B 52, 64 (1995); M.J. Higgins and S. Bhattacharya, Physica C 257, 232 (1996).
28. L.W. Chen, L. Balents, M.P.A. Fisher, and M.C. Marchetti, Phys. Rev. B 54, 12 798 (1996).
29. A. Schmid and W. Hauger, J. Low Temp. Phys. 11, 667 (1973).
30. A.A. Middleton, Phys. Rev. Lett. 68, 670 (1992).
31. O. Narayan and D.S. Fisher, Phys. Rev. B 46, 11 520 (1992).
32. A.A. Middleton, Phys. Rev. B 45, 9465 (1992).
33. D.S. Fisher and D. Huse, Phys. Rev. B 38, 373 (1988); 38, 386 (1988).
34. D.S. Fisher and D. Huse, Phys. Rev. B 38, 373 (1988); 38, 386 (1988).
35. L.B. Ioffe and V.M. Vinokur, J. Phys. C 20, 6149 (1987).
36. M.V. Feigel'man, V.B. Geshkenbein, A.I. Larkin, and V.M. Vinokur, Phys. Rev. Lett. 63, 2303 (1989).
37. T. Nattermann, Phys. Rev. Lett. 64, 2454 (1990).
38. Y.C. Tsai and Y. Shapir, Phys. Rev. E 50, 4445 (1994).
39. L. Radzihovsky, Proceedings of the American Physical Society (talk E37 8), 1998 (unpublished); L. Balents, D. S. Fisher, and L. Radzihovsky (unpublished).
40. L. Radzihovsky, Proceedings of the American Physical Society (talk E37 8), 1998 (unpublished); L. Balents, D. S. Fisher, and L. Radzihovsky (unpublished).
41. P. Chauve, T. Giamarchi, and P. Le Doussal, Europhys. Lett. 44, 110 (1998).
42. L. Balents, D. S. Fisher, and L. Radzihovsky (unpublished).
43. L. Balents and P. Le Doussal, cond-mat/0205358.
44. P.E. Wolf, F. Gallet, S. Balibar, E. Rollet, and Ph. Nozières, J. Phys. (France) 46, 1987 (1985).
45. A. Chowdhury, B.J. Ackerson, and N.A. Clark, Phys. Rev. Lett. 55, 833 (1985), and references therein.
46. Q.-H. Wei, C. Bechinger, D. Rudhardt, and P. Leiderer, Phys. Rev. Lett. 81, 2606 (1998).
47. E. Frey, D.R. Nelson, and L. Radzihovsky, Phys. Rev. Lett. 83, 2977 (1999).
48. L. Radzihovsky, E. Frey, and D.R. Nelson, Phys. Rev. E 63, 031503 (2001).
49. See, for example, C. Reichhardt, and C.J. Olson, cond-mat/0201258 (unpublished); cond-mat/0201021 (unpublished).
50. M.C. Marchetti, A.A. Middleton, and T. Prellberg, Phys. Rev. Lett. 85, 1104 (2000).
51. J.V. José, L.P. Kadanoff, S. Kirkpatrick, and D.R. Nelson, Phys. Rev. B 16, 1217 (1977); 17, 1477(E) (1978).
52. J.V. José, L.P. Kadanoff, S. Kirkpatrick, and D.R. Nelson, Phys. Rev. B 16, 1217 (1977); 17, 1477(E) (1978).
53. S.T. Chui and J.D. Weeks, Phys. Rev. B 14, 4978 (1976); Phys. Rev. Lett. 40, 733 (1978).
54. S.T. Chui and J.D. Weeks, Phys. Rev. B 14, 4978 (1976); Phys. Rev. Lett. 40, 733 (1978).
55. P.B. Wiegmann, J. Phys. C 11, 1583 (1978).
56. T. Ohta and D. Jasnow, Phys. Rev. B 20, 139 (1979).
57. D.J. Amit, Y.Y. Goldshmidt, and G. Grinstein, J. Phys. A 13, 585 (1980).
58. H.J.F. Knops and L.W.J. den Ouden, Physica A 103, 597 (1980).
59. B. Neudecker, Z. Phys. B: Condens. Matter 49, 57 (1982).
60. P. Nozières and F. Gallet, J. Phys. 48, 353 (1987).
61. M. Rost and H. Spohn, Phys. Rev. E 49, 3709 (1994).
62. H. von Beijeren, Phys. Rev. Lett. 38, 993 (1977).
63. T. Hwa, M. Kardar, and M. Paczuski, Phys. Rev. Lett. 66, 441 (1991).
64. M. Kardar, G. Parisi, and Y. C Zhang, Phys. Rev. Lett. 56, 889 (1986).
65. c.
66. R. Seshadri and R.M. Westervelt, Phys. Rev. B 46, 5142 (1992); 46, 5150 (1992).
67. R. Seshadri and R.M. Westervelt, Phys. Rev. B 46, 5142 (1992); 46, 5150 (1992).
68. M.P.A. Fisher, Phys. Rev. Lett. 62, 1415 (1989).
69. Saito, Z. Phys. B 32, 75 (1978).
70. L. Landau and E. Lifshitz, Statistical Physics (Clarendon Press, Oxford, 1938).
71. W.K. Burton, N. Cabrera, and F.C. Frank, Philos. Trans. R. Soc. London, Ser. A 243, 299 (1951).
72. L. Sneddon, M.C. Cross, and D.S. Fisher, Phys. Rev. Lett. 49, 292 (1982).
73. H. Risken, The Fokker-Planck Equation (Springer, Berlin, 1984).
74. S. Scheidl, Z. Phys. B: Condens. Matter 97, 345 (1995).
75. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marychev, Integrals and Series (Gordon and Breach, New York, 1986).
76. Strictly speaking, these changes all take place even at short scales even before a continuum limit is reached. Consequently, at continuum level they are already present, and a careful coarsegraining procedure on the discrete lattice model must be done to derive the continuum nonequilibrium model as was done in Ref. 6.
77. B.I. Halperin, P.C. Hohenberg, and S.K. Ma, Phys. Rev. Lett. 29, 1548 (1972).
78. P.C. Hohenberg and B.I. Halperin, Rev. Mod. Phys. 49, 435 (1977).
79. S. Ma, Modern Theory of Critical Phenomena (Benjamin, New York, 1976).
80. P.C. Martin, E.D. Siggia, and H.A. Rose, Phys. Rev. A 8, 423 (1973); H.K. Janssen, Z. Phys. B 23, 377 (1976); C. De Dominicis and L. Peliti, Phys. Rev. B 18, 353 (1978); R.V. Jensen, J. Stat. Phys. 25, 183 (1981).
81. P.C. Martin, E.D. Siggia, and H.A. Rose, Phys. Rev. A 8, 423 (1973); H.K. Janssen, Z. Phys. B 23, 377 (1976); C. De Dominicis and L. Peliti, Phys. Rev. B 18, 353 (1978); R.V. Jensen, J. Stat. Phys. 25, 183 (1981).
82. P.C. Martin, E.D. Siggia, and H.A. Rose, Phys. Rev. A 8, 423 (1973); H.K. Janssen, Z. Phys. B 23, 377 (1976); C. De Dominicis and L. Peliti, Phys. Rev. B 18, 353 (1978); R.V. Jensen, J. Stat. Phys. 25, 183 (1981).
83. P.C. Martin, E.D. Siggia, and H.A. Rose, Phys. Rev. A 8, 423 (1973); H.K. Janssen, Z. Phys. B 23, 377 (1976); C. De Dominicis and L. Peliti, Phys. Rev. B 18, 353 (1978); R.V. Jensen, J. Stat. Phys. 25, 183 (1981).
84. φ flow even at the lowest order. It is easy to check that the flow equations for the dimensionless couplings involve K(b), γ(b), and p(b) and are independent of the arbitrary choice of z, χ̂, and φ.
85. Y. Saito, Statistical Physics of Crystal Growth (World Scientific, Singapore, 1996).
86. J.M. Kosterlitz and J.M. Thouless, J. Phys. C 6, 1181 (1973).
87. D.R. Nelson and J.M. Kosterlitz, Phys. Rev. Lett. 39, 1201 (1977).
88. J. Villain, J. Phys. (Paris) 36, 581 (1975).
89. E. Frey, D.R. Nelson, and L. Radzihovsky, Phys. Rev. Lett. 83, 2977 (1999); L. Radzihovsky, E. Frey, and D.R. Nelson, Phys. Rev. E 63, 031503 (2001).
90. E. Frey, D.R. Nelson, and L. Radzihovsky, Phys. Rev. Lett. 83, 2977 (1999); L. Radzihovsky, E. Frey, and D.R. Nelson, Phys. Rev. E 63, 031503 (2001).
91. R.G. Petschek and A. Zippelius, Phys. Rev. B 23, 3483 (1981).
92. A.E. Koshelev and V.M. Vinokur, Phys. Rev. Lett. 73, 3580 (1994).
93. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun, (Dover, New York, 1972).
94. M.-C. Cha and H.A. Fertig, Phys. Rev. Lett. 80, 3851 (1998).
95. C. Reichhardt, C.J. Olson, and F. Nori, Phys. Rev. Lett. 78, 2648 (1997); Phys. Rev. B 57, 7937 (1998); C. Reichhardt and F. Nori, Phys. Rev. Lett. 82, 414 (1999); V. Gotcheva and S. Teitel, ibid. 86, 2126 (2126).
96. C. Reichhardt, C.J. Olson, and F. Nori, Phys. Rev. Lett. 78, 2648 (1997); Phys. Rev. B 57, 7937 (1998); C. Reichhardt and F. Nori, Phys. Rev. Lett. 82, 414 (1999); V. Gotcheva and S. Teitel, ibid. 86, 2126 (2126).
97. C. Reichhardt, C.J. Olson, and F. Nori, Phys. Rev. Lett. 78, 2648 (1997); Phys. Rev. B 57, 7937 (1998); C. Reichhardt and F. Nori, Phys. Rev. Lett. 82, 414 (1999); V. Gotcheva and S. Teitel, ibid. 86, 2126 (2126).
98. C. Reichhardt, C.J. Olson, and F. Nori, Phys. Rev. Lett. 78, 2648 (1997); Phys. Rev. B 57, 7937 (1998); C. Reichhardt and F. Nori, Phys. Rev. Lett. 82, 414 (1999); V. Gotcheva and S. Teitel, ibid. 86, 2126 (2126).
99. K.G. Wilson and J. Kogut, Phys. Rep. 12, 75 (1974).
100. F.J. Wegner and A. Houghton, Phys. Rev. A 8, 401 (1973).
101. J.B. Kogut, Rev. Mod. Phys. 51, 659 (1979).
102. c of the ratio K/T unchanged. It is for this reason that conceptually erroneous calculations can and have gotten away with reproducing the usual sine-Gordon (KT) phenomenology.
103. T. Nattermann and L.-H. Tang, Phys. Rev. A 45, 7156 (1992).