Anderson localization on the Cayley tree: Multifractal statistics of the transmission at criticality and off criticality

Journal of Physics A: Mathematical and Theoretical

Volumn 44, Issue 14, 2011, Pages

  Monthus, Cécile ^a   Garel, Thomas ^a  

^a CEA SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79953697724     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/44/14/145001     Document Type: Article

References (59)

1. Anderson P W 1958 Phys. Rev. 109 1492
2. Thouless D J 1974 Phys. Rep. 13 93
3. Thouless D J 1979 Ill Condensed Matter (Les Houches 1978) ed R Balian et al (Amsterdam: North-Holland)
4. Souillard B 1987 Chance and Matter (Les Houches 1986) ed J Souletie et al (Amsterdam: North-Holland)
5. Lifshitz I M, Gredeskul S A and Pastur L A 1988 Introduction to the Theory of Disordered Systems (New York: Wiley)
6. Kramer B and MacKinnon A 1993 Rep. Prog. Phys. 56 1469
7. Markos P 2006 Acta Phys. Slovaca 56 561
8. Evers F and Mirlin A D 2008 Rev. Mod. Phys. 80 1355
9. Abrahams E, Anderson P W, Licciardello D C and Ramakrishnan T V 1979 Phys. Rev. Lett. 42 673
10. Abou-Chacra R, Anderson P W and Thouless D J 1973 J. Phys. C: Solid State Phys. 6 1734
11. see also, Abou-Chacra R and Thouless D J 1974 J. Phys. C: Solid State Phys. 7 65
12. Kunz H and Souillard B 1983 J. Phys. Lett. 44 L411
13. Mirlin A D and Fyodorov Y V 1991 Nucl. Phys. B 366 507
14. Derrida B and Rodgers G J 1993 J. Phys. A: Math. Gen. 26 L457
15. Miller J D and Derrida B 1994 J. Stat. Phys. 75 357
16. Monthus C and Garel T 2009 J. Phys. A: Math. Theor. 42 075002
17. Shapiro B 1983 Phys. Rev. Lett. 50 747
18. Chalker J T and Siak S 1990 J. Phys.: Condens. Matter 2 2671
19. Bell P M and MacKinnon A 1994 J. Phys.: Condens. Matter 6 5423
20. Biroli G, Semerjian G and Tarzia M 2010 Prog. Theor. Phys. Suppl. 184 187
21. Basko D M, Aleiner I L and Altshuler B L 2006 Ann. Phys. 321 1126
22. Basko D M, Aleiner I L and Altshuler B L 2007 Phys. Rev. B 76 052203
23. Altshuler B L, Gefen Y, Kamenev A and Levitov L S 1997 Phys. Rev. Lett. 78 2803
24. Silvestrov P G 1997 Phys. Rev. Lett. 79 3994
25. Silvestrov P G 1998 Phys. Rev. E 58 5629
26. Silvestrov P G 2001 Phys. Rev. B 64 113309
27. Gornyi I V, Mirlin A D and Polyakov D G 2005 Phys. Rev. Lett. 95 206603
28. Oganesyan V and Huse D A 2007 Phys. Rev. B 75 155111
29. Monthus C and Garel T 2010 Phys. Rev. B 81 134202
30. Znidaric M, Prosen T and Prelovsek P 2008 Phys. Rev. B 77 064426
31. Karahalios A, Metavitsiadis A, Zotos X, Gorczyca A and Prelovsek P 2009 Phys. Rev. B 79 024425
32. Barisic O S and Prelovsek P 2010 Phys. Rev. B 82 161106
33. Berkelbach T C and Reichman D R 2010 Phys. Rev. B 81 224429
34. Pal A and Huse D A 2010 Phys. Rev. B 82 174411
35. Barisic O S and Prelovsek P 2010 Phys. Rev. B 82 161106
36. Landauer R 1970 Phil. Mag. 21 863
37. Anderson P W, Thouless D J, Abrahams E and Fisher D S 1980 Phys. Rev. B 22 3519
38. Anderson P W and Lee P A 1980 Prog. Theor. Phys. Suppl. 69 212
39. Luck J M 1992 Systèmes Désordonnés Unidimensionnels (Saclay: Alea)
40. Stone A D and Szafer A 1988 IBM J. Res. Dev. 32 384
41. Aizenman M and Warzel S 2010 arXiv:1010.2673
42. Derrida B and Spohn H 1988 J. Stat. Phys. 51 817
43. Halpin-Healy T and Zhang Y-C 1995 Phys. Rep. 254 215
44. Cook J and Derrida B 1991 J. Stat. Phys. 63 505
45. Derrida B 1981 Phys. Rev. B 24 2613
46. Derrida B 1994 Non-self-averaging effects in sums of random variables, spin glasses, random maps and random walks On Three Levels ed M Fannes et al (New York: Plenum)
47. Chhabra A and Jensen R V 1989 Phys. Rev. Lett. 62 1327
48. Chamon C, Mudry C and Wen X-G 1996 Phys. Rev. Lett. 77 4194
49. Castillo H E, Chamon C, Fradkin E, Goldbart P M and Mudry C 1997 Phys. Rev. B 56 10668
50. Carpentier D and Le Doussal P 1998 Phys. Rev. Lett. 81 2558
51. Carpentier D and Le Doussal P 2000 Nucl. Phys. B 588 565
52. Carpentier D and Le Doussal P 2001 Phys. Rev. E 63 026110
53. Fyodorov Y V and Bouchaud J P 2007 JETP Lett. 86 487
54. Fyodorov Y V and Bouchaud J P 2008 J. Phys. A: Math. Theor. 41 324009
55. Fyodorov Y V and Bouchaud J P 2008 J. Phys. A: Math Theor. 41 372001
56. Fyodorov Y V 2009 J. Stat. Mech. P07022
57. Fyodorov Y V, Le Doussal P and Rosso A 2009 J. Stat. Mech. P10005
58. Fyodorov Y V 2010 Physica A 389 4229
59. Lloyd P 1969 J. Phys. C: Solid State Phys. 2 1717