One-parameter scaling theory for stationary states of disordered nonlinear systems

Physical Review Letters

Volumn 104, Issue 16, 2010, Pages

  Bodyfelt, Joshua D ^a,b,c   Kottos, Tsampikos ^a   Shapiro, Boris ^d  

^a WESLEYAN UNIVERSITY   (United States)

^b MPI for Dynamics and Self Organization   (Germany)

^c MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^d TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ANDERSON LOCALIZATION; NON-LINEARITY; NONLINEAR LATTICES; ONE-PARAMETER SCALING; SCALING THEORIES; STATIONARY SOLUTIONS; STATIONARY STATE; THEORETICAL ARGUMENTS;

NUMERICAL ANALYSIS;

NONLINEAR SYSTEMS;

EID: 77951261509     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.104.164102     Document Type: Article

References (44)

1. P. Anderson, Phys. Rev. 109, 1492 (1958). PHRVAO 0031-899X 10.1103/PhysRev.109.1492
2. D.S. Wiersma, Nature (London) NATUAS 0028-0836 390, 671 (1997). 10.1038/37757
3. A.A. Chabanov, M. Stoytchev, and A.Z. Genack, Nature (London) NATUAS 0028-0836 404, 850 (2000). 10.1038/35009055
4. M. Störzer, Phys. Rev. Lett. 96, 063904 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.063904
5. J. Bodyfelt, Phys. Rev. Lett. 102, 253901 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.253901
6. H. Hu, Nature Phys. NPAHAX 1745-2473 4, 945 (2008). 10.1038/nphys1101
7. H. Cao, Phys. Rev. Lett. 82, 2278 (1999); PRLTAO 0031-9007 10.1103/PhysRevLett.82.2278
8. H. Cao, Waves Random Media 13, R1 (2003). WRMEEV 0959-7174 10.1088/0959-7174/13/3/201
9. Y. Lahini, Phys. Rev. Lett. 100, 013906 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.013906
10. T. Pertsch, Phys. Rev. Lett. 93, 053901 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.053901
11. T. Schwartz, Nature (London) NATUAS 0028-0836 446, 52 (2007). 10.1038/nature05623
12. A. Aspect, Nature (London) NATUAS 0028-0836 453, 891 (2008). 10.1038/nature07000
13. G. Roati, Nature (London) NATUAS 0028-0836 453, 895 (2008). 10.1038/nature07071
14. A.R. Bishop, Disorder and Nonlinearity (Springer-Verlag, Berlin, 1989).
15. F.K. Abdullaev, Nonlinearity With Disorder (Springer, Berlin, 1992).
16. A.R. Bishop, Fluctuation Phenomena: Disorder and Nonlinearity (World Scientific, Singapore, 1995).
17. M.I. Molina and G.P. Tsironis, Int. J. Mod. Phys. B 9, 1899 (1995). IJPBEV 0217-9792 10.1142/S021797929500077X
18. S.A. Gredeskul and Y.S. Kivshar, Phys. Rep. 216, 1 (1992); PRPLCM 0370-1573 10.1016/0370-1573(92)90023-S
19. T. Paul, Phys. Rev. Lett. 98, 210602 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.98.210602
20. T. Kottos and M. Weiss, Phys. Rev. Lett. 93, 190604 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.190604
21. D.L. Shepelyansky, Phys. Rev. Lett. 70, 1787 (1993); PRLTAO 0031-9007 10.1103/PhysRevLett.70.1787
22. B. Shapiro, Phys. Rev. Lett. 99, 060602 (2007); PRLTAO 0031-9007 10.1103/PhysRevLett.99.060602
23. G. Kopidakis, Phys. Rev. Lett. 100, 084103 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.100.084103
24. A.S. Pikovsky and D.L. Shepelyansky, Phys. Rev. Lett. 100, 094101 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.100.094101
25. S.E. Skipetrov, Phys. Rev. Lett. 100, 165301 (2008); PRLTAO 0031-9007 10.1103/PhysRevLett.100.165301
26. S. Flach D.O. Krimer, and Ch. Skokos, Phys. Rev. Lett. 102, 024101 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.024101
27. J. Fröhlich, T. Spencer, and C.E. Wayne, J. Stat. Phys. 42, 247 (1986); JSTPSB 0022-4715 10.1007/BF01127712
28. C. Albanese and J. Fröhlich, Commun. Math. Phys. 116, 475 (1988); CMPHAY 0010-3616 10.1007/BF01229204
29. C. Albanese, J. Fröhlich, and T. Spencer, Commun. Math. Phys. 119, 677 (1988); CMPHAY 0010-3616 10.1007/BF01218350
30. C. Albanese and J. Fröhlich, Commun. Math. Phys. 138, 193 (1991). CMPHAY 0010-3616 10.1007/BF02099674
31. G. Kopidakis and S. Aubry, Phys. Rev. Lett. 84, 3236 (2000); PRLTAO 0031-9007 10.1103/PhysRevLett.84.3236
32. J.F.R. Archilla, R.S. MacKay, and J.L. Marín, Physica (Amsterdam) 134D, 406 (1999). PDNPDT 0167-2789 10.1016/S0167-2789(99)00131-1
33. S. Fishman, A. Iomin, and K. Mallick, Phys. Rev. E PLEEE8 1539-3755 78, 066605 (2008); 10.1103/PhysRevE.78.066605
34. A. Iomin and S. Fishman, Phys. Rev. E PLEEE8 1539-3755 76, 056607 (2007). 10.1103/PhysRevE.76.056607
35. F. Evers and A.D. Mirlin, Rev. Mod. Phys. 80, 1355 (2008). RMPHAT 0034-6861 10.1103/RevModPhys.80.1355
36. G. Casati, L. Molinari, and F. Izrailev, Phys. Rev. Lett. 64, 1851 (1990). PRLTAO 0031-9007 10.1103/PhysRevLett.64.1851
37. Y.V. Fyodorov and A.D. Mirlin, Phys. Rev. Lett. 69, 1093 (1992); PRLTAO 0031-9007 10.1103/PhysRevLett.69.1093
38. A.D. Mirlin and Y.V. Fyodorov, J. Phys. A JPHAC5 0305-4470 26, L551 (1993); 10.1088/0305-4470/26/12/012
39. Y.V. Fyodorov and A.D. Mirlin, Int. J. Mod. Phys. B IJPBEV 0217-9792 8, 3795 (1994). 10.1142/S0217979294001640
40. G. Casati, I. Guarneri, F. Izrailev, S. Fishman, and L. Molinari, J. Phys. Condens. Matter JCOMEL 0953-8984 4, 149 (1992); 10.1088/0953-8984/4/1/024
41. F.M. Izrailev, T. Kottos, and G.P. Tsironis, J. Phys. Condens. Matter JCOMEL 0953-8984 8, 2823 (1996). 10.1088/0953-8984/8/16/012
42. B. Kramer and A. MacKinnon, Rep. Prog. Phys. 56, 1469 (1993). RPPHAG 0034-4885 10.1088/0034-4885/56/12/001
43. Y. Alhassid and R.D. Levine, Phys. Rev. Lett. 57, 2879 (1986). PRLTAO 0031-9007 10.1103/PhysRevLett.57.2879
44. J. Bodyfelt, T. Kottos, and B. Shapiro (to be published).