Localization-delocalization transition for disordered cubic harmonic lattices

Journal of Physics Condensed Matter

Volumn 24, Issue 40, 2012, Pages

  Pinski, S D ^a   Schirmacher, W ^b,c   Whall, T ^a   Romer R A ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^c JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANDERSON MODELS; CRITICAL EXPONENT; CUBIC LATTICE; DENSITY OF STATE; HARMONIC COUPLINGS; HARMONIC LATTICE; LOCALIZATION LENGTH; LOCALIZATION-DELOCALIZATION TRANSITIONS; SPRING CONSTANTS; UNIVERSALITY CLASS; UNSTABLE WAVES;

SPRINGS (COMPONENTS);

PHASE BOUNDARIES;

ARTICLE; CHEMICAL MODEL; CHEMICAL STRUCTURE; COMPUTER SIMULATION; CONFORMATION; PHASE TRANSITION;

COMPUTER SIMULATION; MODELS, CHEMICAL; MODELS, MOLECULAR; MOLECULAR CONFORMATION; PHASE TRANSITION;

EID: 84866514731     PISSN: 09538984     EISSN: 1361648X     Source Type: Journal    
DOI: 10.1088/0953-8984/24/40/405401     Document Type: Article

References (81)

1. Anderson P W 1958 Absence of diffusion in certain random lattices Phys. Rev. 109 1492-505
2. Lee P A and Ramakrishnan T V 1985 Disordered electronic systems Rev. Mod. Phys. 57 287-337
3. Kramer B and MacKinnon A 1993 Localization: theory and experiment Rep. Prog. Phys. 56 1469-564
4. Belitz D and Kirkpatrick T R 1994 The Anderson-Mott transition Rev. Mod. Phys. 66 261-380 (Pubitemid 24793178)
5. Evers F and Mirlin A D 2008 Anderson transitions Rev. Mod. Phys. 80 1355-417
6. Billy J, Josse V, Zuo Z, Bernard A, Hambrecht B, Lugan P, Clement D, Sanchez-Palencia L, Bouyer P and Aspect A 2008 Direct observation of Anderson localization of matter waves in a controlled disorder Nature 453 891-4 (Pubitemid 351832566)
7. Roati G, DErrico C, Fallani L, Fattori M, Fort C, Zaccanti M, Modugno G, Modugno M and Inguscio M 2008 Anderson localization of a non-interacting Bose-Einstein condensate Nature 453 895-9 (Pubitemid 351832573)
8. Faez S, Strybulevych A, Page J H, Lagendijk A and van Tiggelen B A 2009 Observation of multifractality in Anderson localization of ultrasound Phys. Rev. Lett. 103 155703
9. Schirmacher W, Diezemann G and Ganter C 1998 Harmonic vibrational excitations in disordered solids and the boson peak Phys. Rev. Lett. 81 136-9 (Pubitemid 128653208)
10. Kantelhardt J W, Russ S and Bunde A 2001 Excess modes in the vibrational spectrum of disordered systems and the boson peak Phys. Rev. B 63 064302
11. Pinski S D, Schirmacher W and Römer R A 2012 Anderson universality in a model of disordered phonons Europhys. Lett. 97 16007
12. Russ S 2002 Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder Phys. Rev. B 66 012204
13. Schirmacher W and Diezemann G 1999 Propagation and localisation of vibrational modes in three-dimensional disordered systems: the binary force constant model Ann. Phys., Lpz. 8 727-32 (Pubitemid 30517835)
14. Feldman J L, Kluge M D, Allen P B and Wooten F 1993 Thermal conductivity and localization in glasses: numerical study of a model of amorphous silicon Phys. Rev. B 48 12589-602
15. Sarkar S K, Matharoo G S and Pandey A 2004 Universality in the vibrational spectra of single-component amorphous clusters Phys. Rev. Lett. 92 215503
16. Canisius J and van Hemmen J L 1985 Localization of phonons J. Phys. C: Solid State Phys. 18 4873-84
17. Ludlam J J, Stadelmann T O, Taraskin S N and Elliott S R 2001 Numerical analysis of the vibrational eigenmodes of a 2D disordered lattice J. Non-Cryst. Solids 293 676-81 (Pubitemid 32997897)
18. Shima H, Nishino S and Nakayama T 2007 Peculiar behaviours of excited modes in harmonic chains with correlated disorder J. Phys. Conf. Ser. 92 012156
19. Ludlam J J, Taraskin S N and Elliott S R 2003 Disorder induced vibrational localization Phys. Rev. B 67 132203
20. Bembenek S D and Laird B B 1995 Instantaneous normal modes and the glass transition Phys. Rev. Lett. 74 936-9
21. Bembenek S D and Laird B B 1996 The role of localization in glasses and supercooled liquids J. Chem. Phys. 104 5199-208 (Pubitemid 126717120)
22. Huang B J and Wu T 2010 Multifractality of instantaneous normal modes at mobility edges Phys. Rev. E 82 051133
23. Huang B J and Wu T 2009 Localization-delocalization transition in Hessian matrices of topologically disordered systems Phys. Rev. E 79 041105
24. Liu Z, Zhang X, Mao Y, Zhu Y Y, Yang Z, Chan C T and Sheng P 2000 Locally resonant sonic materials Science 289 1734
25. Hirsekorn M 2004 Small-size sonic crystals with strong attenuation bands in the audible frequency range Appl. Phys. Lett. 84 3364-6
26. Chan C T, Li J and Fung K H 2006 On extending the concept of double negativity to acoustic waves Science A 7 24-8
27. Zhang S, Yin L and Fang N 2009 Focusing ultrasound with an acoustic metamaterial network Phys. Rev. Lett. 102 194301
28. Ding Y, Liu Z, Qiu C and Shi J 2007 Metamaterials with simultaneously negative bulk modulus and mass density Phys. Rev. Lett. 99 093904 (Pubitemid 47357775)
29. Wright D W and Cobbold R S C 2009 The characteristics and applications of metamaterials Ultrasound 17 68-73
30. Bulka B, Schreiber M and Kramer B 1987 Localization, quantum interference, and the metal-insulator transition Z. Phys. B 66 21
31. Akita Y and Ohtsuki T 1998 Anderson transition of three dimensional phonon modes J. Phys. Soc. Japan 67 2954-5
32. Born M and Huang K 1954 Dynamical Theory of Crystal Lattices (New York: Oxford University Press)
33. Srivastava G P 1990 The Physics of Phonons (New York: Taylor and Francis)
34. Brandes T and Kettemann S (ed) 2003 The Anderson Transition and its Ramifications - Localisation, Quantum Interference, and Interactions (Springer Lecture Notes in Physics vol 630) (Berlin: Springer)
35. Grussbach H and Schreiber M 1995 Determination of the mobility edge in the Anderson model of localization in three dimensions by multifractal analysis Phys. Rev. B 51 663-6
36. Madan B and Keyes T 1993 Unstable modes in liquids density of states, potential energy, and heat capacity J. Chem. Phys. 98 3342
37. Pinski S D and Römer R A 2011 Study of the localization- delocalization transition for phonons via transfer matrix method techniques J. Phys. Conf. Ser. 286 012025
38. Lehoucq R B, Sorensen D C and Yang C 1998 Arpack Users Guide: Solution of Large-Scale Eigenvalue Problems With Implicityly Restorted Arnoldi Methods (Philadelphia, PA: Society for Industrial Mathematics)
39. Schenk O, Bollhöfer M and Römer R 2006 On large scale diagonalization techniques for the Anderson model of localization SIAM J. Sci. Comput. 28 963 (Pubitemid 46785411)
40. Vasquez L J, Rodriguez A and Römer R A 2008 Multifractal analysis of critical states in the 3D Anderson model. I. Symmetry relation under typical averaging Phys. Rev. B 78 195106
41. Ludlam J J, Taraskin S N, Elliot S R and Drabold D A 2005 Universal features of localized eigenstates in disordered systems J. Phys.: Condens. Matter 17 L321-7
42. Mirlin A D, Fyodorov Y V, Mildenberger A and Evers F 2006 Exact relations between multifractal exponents at the Anderson transition Phys. Rev. Lett. 97 046803 (Pubitemid 44147307)
43. Anderson E et al 1987 LAPACK Users Guide (Philadelphia, PA: Society for Industrial Mathematics)
44. Léonforte F, Tanguy A, Wittmer J P and Barrat J-L 2006 Inhomogeneous elastic response of silica glass Phys. Rev. Lett. 97 055501 (Pubitemid 44156703)
45. Léonforte F, Boissiére R, Tanguy A, Wittmer J P and Barrat J-L 2005 Continuum limit of amorphous elastic bodies. III. Three-dimensional systems Phys. Rev. B 72 224206 (Pubitemid 43022613)
46. Monaco G and Mossa S 2009 Anomalous properties of the acoustic excitations in glasses on the mesoscopic length scale Proc. Natl Acad. Sci. 106 16907-12
47. Yonezawa F and Morigaki K 1973 Coherent potential approximation: basic concepts and applications Prog. Theor. Phys. Suppl. 53 1-76
48. Taraskin S N and Elliott S R 2002 Disorder-induced zero-energy spectral singularity for random matrices with correlations Phys. Rev. B 65 052201
49. Scopigno T, Suck J B, Angelini R, Albergamo F and Ruocco G 2006 High-frequency dynamics in metallic glasses Phys. Rev. Lett. 96 135501
50. Taraskin S N, Ludlam J J, Natarajan G and Elliott S R 2002 Propagation, hybridization and localization of vibrational excitations in disordered materials Phil. Mag. B 82 197-208 (Pubitemid 35388462)
51. Monthus C and Garel T 2010 Anderson localization of phonons in dimension d = 1,2,3: finite-size properties of the inverse participation ratios and eigenstates Phys. Rev. B 81 224208
52. Mehta M L 1991 Random Matrices and the Statistical Theory of Energy Levels (New York: Academic)
53. Haake F 1992 Quantum Signatures of Chaos 2nd edn (Berlin: Springer)
54. Porter C E 1965 Statistical Theories of Spectra: Fluctuations (New York: Academic)
55. Dyson F J 1962 Statistical theory of the energy levels of complex systems. I J. Math. Phys. 3 140-56
56. Fyodorov Y V and Mirlin A D 1994 Statistical properties of eigenfunctions of random quasi 1D one-particle Hamiltonians Int. J. Mod. Phys. B 8 3795
57. Uski V, Mehlig B, Römer R A and Schreiber M 2000 An exact diagonalization study of rare events in disordered conductors Phys. Rev. B 62 R7699-702 (Pubitemid 32366532)
58. Mirlin A D 2000 Statistics of energy levels and eigenfunctions in disordered systems Phys. Rep. 326 259-382
59. Nikolić B K 2001 Statistical properties of eigenstates in three-dimensional mesoscopic systems with off-diagonal or diagonal disorder Phys. Rev. B 64 014203
60. Müller K, Mehlig B, Milde F and Schreiber M 1997 Statistics of wave functions in disordered and in classically chaotic systems Phys. Rev. Lett. 78 215-8 (Pubitemid 127647432)
61. Cain P, Römer R A and Schreiber M 1999 Phase diagram of the three-dimensional Anderson model of localization with random hopping Ann. Phys., Lpz. 8 SI33-6
62. Biswas P, Cain P, Römer R A and Schreiber M 2000 Off-diagonal disorder in the Anderson model of localization Phys. Status Solidi b 218 205-9
63. Cain P 1998 Das Anderson-Modell der Lokalisierung mit nichtdiagonaler Unordnung Masters Thesis Technische Universität Chemnitz
64. MacKinnon A and Kramer B 1981 One-parameter scaling of localization length and conductance in disordered systems Phys. Rev. Lett. 47 1546-9
65. Kramer B, Broderix A, MacKinnon A and Schreiber M 1990 The Anderson transition: new numerical results for the critical exponents Physica A 167 163-74
66. Slevin K and Ohtsuki T 1999 Corrections to scaling at the Anderson transition Phys. Rev. Lett. 82 382-5 (Pubitemid 129583625)
67. MacKinnon A 1994 Critical exponents for the metal-insulator transition J. Phys.: Condens. Matter 6 2511-8
68. Rodriguez A, Vasquez L J, Slevin K and Römer R A 2010 Critical parameters from a generalized multifractal analysis at the Anderson transition Phys. Rev. Lett. 105 046403
69. Ludlam J J 2004 Localisation of the vibrations of amorphous materials PhD Thesis University of Cambridge
70. Rodriguez A, Vasquez L J, Slevin K and Römer R A 2011 Multifractal finite-size scaling and universality at the anderson transition Phys. Rev. B 84 134209
71. Rodriguez A, Vasquez L J and Römer R A 2008 Multifractal analysis of critical states in the 3D Anderson model. II. Symmetry relation under ensemble averaging Phys. Rev. B 78 195107
72. Clark A M, Miller N A, Williams A, Ruggiero S T, Hilton G C, Vale L R, Beall J A, Irwin K D and Ullom J N 2005 Cooling of bulk material by electron-tunneling refrigerators Appl. Phys. Lett. 86 173508 (Pubitemid 40865932)
73. Zebarjadi M, Esfarjani K, Dresselhaus M S, Ren Z F and Chen G 2012 Perspectives on thermoelectrics: from fundamentals to device applications Energy Environ. Sci. 5 5147-62
74. Fang N, Xi D, Xu J, Ambati M, Srituravanich W, Sun C and Zhang X 2006 Ultrasonic metamaterials with negative modulus Nature Mater. 5 452-6 (Pubitemid 43838907)
75. Yao S, Zhou X and Hu G 2008 Experimental study on negative effective mass in a 1D mass-spring system New J. Phys. 10 043020
76. Huang H H and Sun C T 2009 Wave attenuation mechanism in an acoustic metamaterial with negative effective mass density New J. Phys. 11 013003
77. He Z, Qiu C, Cheng L, Xiao M, Deng K and Liu Z 2010 Negative-dynamic-mass response without localized resonance Europhys. Lett. 91 54004
78. Joyce G S 1973 On the simple cubic lattice Green function Phil. Trans. R. Soc. A 273 583-610
79. Yonezawa F 1968 A systematic approach to the problems of random lattices. I: a self-contained first-order approximation taking into account the exclusion effect Prog. Theor. Phys. 40 734
80. Wooszyn M and Maksymowicz A Z 2002 Coherent potential approximation technique in a simple example of resistivity calculations for binary alloys Task Q. 6 669-80
81. Oseledec V I 1968 A multiplicative ergodic theorem. Ljapunov characteristic numbers for dynamical systems Trans. Mosc. Math. Soc. 19 197-231