Applications of Ideas from Random Matrix Theory to Step Distributions on "Misoriented" Surfaces

Annales Henri Poincare

Volumn 4, Issue SUPPL. 2, 2003, Pages

  Einstein, T L ^a  

^a Bldg 142   (United States)

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EID: 0346343016     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-003-0964-4     Document Type: Article

References (53)

1. M.L. Mehta, Random Matrices, 2nd ed. (Academic, New York, 1991).
2. V.B. Shenoy, S.W. Zhang, and W.F Saam, Phys. Rev. Lett. 81, 3475 (1998); Surface Sci. 467, 58 (2000).
3. V.B. Shenoy, S.W. Zhang, and W.F Saam, Phys. Rev. Lett. 81, 3475 (1998); Surface Sci. 467, 58 (2000).
4. V.L. Pokrovsky and A.L. Talapov, Theory of Incommensurate Crystals (Harwood Academic, New York, 1984).
5. M.E. Fisher, J. Stat. Phys. 34, 667 (1984) and pvt. comm.
6. J.M. Rickman and D.J. Srolovitz, Surface Sci. 284, 211 (1993).
7. V.I. Marchenko and A.Ya. Parshin, Sov. Phys. JETP 52, 129 (1980).
8. 2 [8, 9].
9. C. Jayaprakash, C. Rottman, and W.F. Saam, Phys. Rev. B 30, 6549 (1984); E.D. Williams, R.J. Phaneuf, J. Wei, N.C. Bartelt, and T.L. Einstein, Surface Sci. 310, 451 (1994).
10. C. Jayaprakash, C. Rottman, and W.F. Saam, Phys. Rev. B 30, 6549 (1984); E.D. Williams, R.J. Phaneuf, J. Wei, N.C. Bartelt, and T.L. Einstein, Surface Sci. 310, 451 (1994).
11. See P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics (Cambridge Univ. Press, Cambridge, 1995), chap. 10.5.1, and references therein, for general background.
12. R.C. Redfield and A. Zangwill, Phys. Rev. B 46, 4289 (1992).
13. T.L. Einstein, in: Handbook of Surface Science, vol. 1, W.N. Unertl, ed. (Elsevier Science B.V., Amsterdam, 1996), chap. 11.
14. H.-C. Jeong, E.D. Williams, Surf. Sci. Rep. 34, 171 (1999).
15. E.E. Gruber and W.W. Mullins, J. Phys. Chem. Solids 28, 875 (1967).
16. N.C. Bartelt, T.L. Einstein, and E.D. Williams, Surface Sci. 240, L591 (1990).
17. X.-S. Wang, J.L. Goldberg, N.C. Bartelt, T.L. Einstein, and E.D. Williams, Phys. Rev. Lett. 65, 2430 (1990).
18. C. Alfonso, J.M. Bermond, J.C. Heyraud, and J.-J. Métois, Surface Sci. 262, 371 (1992).
19. T. Ihle, C. Misbah, and O. Pierre-Louis, Phys. Rev. B 58, 2289 (1998).
20. L. Masson, L. Barbier, J. Cousty, and B. Salanon, Surface Sci. 317, L1115 (1994); L. Barbier, L. Masson, J. Cousty, and B. Salanon, Surface Sci. 345, 197 (1996); E. Le Goff, L. Barbier. L. Masson, and B. Salanon, Surface Sci. 432, 139 (1999).
21. L. Masson, L. Barbier, J. Cousty, and B. Salanon, Surface Sci. 317, L1115 (1994); L. Barbier, L. Masson, J. Cousty, and B. Salanon, Surface Sci. 345, 197 (1996); E. Le Goff, L. Barbier. L. Masson, and B. Salanon, Surface Sci. 432, 139 (1999).
22. L. Masson, L. Barbier, J. Cousty, and B. Salanon, Surface Sci. 317, L1115 (1994); L. Barbier, L. Masson, J. Cousty, and B. Salanon, Surface Sci. 345, 197 (1996); E. Le Goff, L. Barbier. L. Masson, and B. Salanon, Surface Sci. 432, 139 (1999).
23. J.F. van Diejen and L. Vinet, eds., Calogero-Moser-Sutherland Models (Springer-Verlag, New York, 2000).
24. F. Calogero, J. Math. Phys. 10 2191, 2197 (1969).
25. B. Sutherland, J. Math. Phys. 12, 246 (1971).
26. B. Sutherland, Phys. Rev. A 4, 2019 (1971).
27. T. Guhr, A.Müller-Groeling, and H.A. Weidenmüller. Phys. Rep. 299, 189 (1998).
28. F. J. Dyson, Commun. Math. Phys. 12, 91 (1969).
29. F. J. Dyson, J. Math. Phys. 3, 140, 157 (1962).
30. F. J. Dyson, Commun. Math. Phys. 19, 235 (1970).
31. B. Joós, T.L. Einstein, and N.C. Bartelt, Phys. Rev. 543, 8153 (1991).
32. T. L. Einstein and O. Pierre-Louis, Surface Sci. 424, L299 (1999).
33. For explicit details see, e.g., Zwerger, in: T. Dittrich, P. Hänggi, G.-L. Ingold, B. Kramer, G. Schön, and W. Zwerger, Quantum Transport and Dissipation (Wiley-VCH, Weinheim, 1998), chap. 1.
34. F. Haake, Quantum Signatures of Chaos (Springer. Berlin, 1991), esp. Fig. 4.2a.
35. T.L. Einstein, H.L. Richards, S.D. Cohen, and O. Pierre-Louis, Surface Sci. 493, 460 (2001).
36. Hailu Gebremariam, S.D. Cohen. H.L. Richards, and T.L. Einstein, preprint.
37. H.L. Richards, S.D. Cohen, T.L. Einstein, and M. Giesen, Surface Sci. 453, 59 (2000).
38. M. Giesen and T.L. Einstein, Surface Sci. 449, 191 (2000).
39. V.Ya. Krivnov and A.A. Ovchinnikov, Sov. Phys. JETP 55, 162 (1982).
40. D. Sen and R. K. Bhaduri, Can. J. Phys. 77, 327 (1999).
41. P.J. Forrester, Nucl. Phys. B388, 671 (1992); J. Stat. Phys. 72, 39 (1993).
42. P.J. Forrester, Nucl. Phys. B388, 671 (1992); J. Stat. Phys. 72, 39 (1993).
43. The ratio is a slowly decreasing function of β, around 1.04 at β=1, crossing 1 around β=4, and around 0.97 around β=10.
44. Z.N.C. Ha, Nucl. Phys. B435[FS], 604 (1995).
45. F.D.M. Haldane, in: Correlation Effects in Low-Dimensional Electronic Systems, A. Okiji and N. Kawakami, eds. (Springer, Berlin, 1994). 3.
46. See also F. Lesage, V. Pasquier, and D. Serban, Nucl. Phys. B435 [FS], 585 (1995).
47. D. M. Gangardt and A. Kamenev, Nucl. Phys. B610[PM], 578 (2001).
48. S.D. Cohen, R.D. Schroll, T.L. Einstein, J.-J. Métois, Hailu Gebremariam, H.L. Richards, and E.D. Williams, Phys. Rev. B 66. 115310 (2002); R.D. Schroll et al., Appl. Surface Sci. 212-213C, 219 (2003).
49. S.D. Cohen, R.D. Schroll, T.L. Einstein, J.-J. Métois, Hailu Gebremariam, H.L. Richards, and E.D. Williams, Phys. Rev. B 66. 115310 (2002); R.D. Schroll et al., Appl. Surface Sci. 212-213C, 219 (2003).
50. H.L. Richards and T.L. Einstein, Phys. Rev. E, submitted [cond-mat/0008089].
51. A.A. Drǎgulescu and V.M. Yakovenko, cond-mat/0203046.
52. S. Dieluweit, M. Giesen, H. Ibach, and T.L. Einstein, Phys. Rev. B 67, 121410 (R) (2003).
53. J. Villain, D.R. Grempel, and J. Lapujoulade, J. Phys. F 15, 809 (1985).