Erratum: Aging Wiener-Khinchin theorem and critical exponents of 1/ f β noise (Physical Review E (2016) 94 (052130) DOI: 10.1103/PhysRevE.94.052130);Aging Wiener-Khinchin theorem and critical exponents of 1/fβ noise

Physical Review E

Volumn 94, Issue 5, 2016, Pages

  Leibovich, N ^a   Dechant, A ^a,b   Lutz, E ^b   Barkai, E ^a  

^a BAR ILAN UNIVERSITY   (Israel)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN MOVEMENT; FOURIER SERIES; POWER SPECTRUM; QUANTUM OPTICS; SEMICONDUCTOR QUANTUM DOTS;

AUTOCORRELATION FUNCTIONS; INFRARED DIVERGENCES; LOGARITHMIC POTENTIALS; NONANALYTIC FUNCTIONS; NONSTATIONARY PROCESS; SINGLE FILE DIFFUSION; TIME-DEPENDENT SPECTRUM; WIENER-KHINCHIN THEOREM;

AUTOCORRELATION;

EID: 84996841713     PISSN: 24700045     EISSN: 24700053     Source Type: Journal    
DOI: 10.1103/PhysRevE.96.059902     Document Type: Erratum

References (83)

1. R. Kubo, M. Toda, and H. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer, Berlin, 1995).
2. M. B. Priestley, Spectral Analysis and Time Series (Academic, London, 1981).
3. I. Eliazar and J. Klafter, Universal Generation of Statistical Self-Similarity: A Randomized Central Limit Theorem, Phys. Rev. Lett. 103, 040602 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.040602
4. G. Aquino, M. Bologna, P. Grigolini, and B. J. West, Beyond the Death of Linear Response: 1/f Optimal Information Transport, Phys. Rev. Lett. 105, 040601 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.040601
5. M. Niemann, H. Kantz, and E. Barkai, Fluctuations of 1/f Noise and the Low-Frequency Cutoff Paradox, Phys. Rev. Lett 110, 140603 (2013). 10.1103/PhysRevLett.110.140603
6. M. A. Rodríguez, Complete spectral scaling of time series: Towards a classification of 1/f noise, Phys. Rev. E 90, 042122 (2014). PLEEE8 1539-3755 10.1103/PhysRevE.90.042122
7. C. Monthus and J-P. Bouchaud, Models of traps and glass phenomenology, J. Phys. A: Math. Gen. 29, 3847 (1996). JPHAC5 0305-4470 10.1088/0305-4470/29/14/012
8. L. Silvestri, L. Fronzoni, P. Grigolini, and P. Allegrini, Event-Driven Power-Law Relaxation in Weak Turbulence, Phys. Rev. Lett. 102, 014502 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.014502
9. J. Schriefl, M. Clusel, D. Carpentier, and P. Degiovanni, Dephasing by a nonstationary classical intermittent noise, Phys. Rev. B 72, 035328 (2005). PRBMDO 1098-0121 10.1103/PhysRevB.72.035328
10. A. Barrat, R. Burioni, and M. Mezard, Ageing classification in glassy dynamics, J. Phys. A: Math. Gen. 29, 1311 (1996) JPHAC5 0305-4470 10.1088/0305-4470/29/7/005;
11. J. P. Bouchaud, L. F. Cugliandolo, J. Kurchan, and M. Mézard, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1998).
12. L. Bellon and S. Ciliberto, Experimental study of the fluctuation dissipation relation during an aging process, Physica D (Amsterdam) 168-169, 325 (2002). PDNPDT 0167-2789 10.1016/S0167-2789(02)00520-1
13. L. F. Cugliandolo, J. Kurchan, and G. Parisi, Off equilibrium dynamics and aging in unfrustrated systems, J. Phys. I 4 (11), 1641 (1994). 10.1051/jp1:1994212
14. L. F. Cugliandolo, J. Kurchan, and L. Peliti, Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics, Phys. Rev. E 55, 3898 (1997). 1063-651X 10.1103/PhysRevE.55.3898
15. A. Crisanti and F. Ritort, Violation of the fluctuation dissipation theorem in glassy systems: basic notions and the numerical evidence, J. Phys. A: Math. Gen. 36, R181 (2003). JPHAC5 0305-4470 10.1088/0305-4470/36/21/201
16. D. S. Dean, A. Iorio, E. Marinari, and G. Oshanin, Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model, Phys. Rev. E. 94, 032131 (2016). 10.1103/PhysRevE.94.032131
17. L. Cohen, Time-frequency distributions-a review, Proc. IEEE 77 (7), 941 (1989). IEEPAD 0018-9219 10.1109/5.30749
18. C. H. Page, Instantaneous power spectra, J. Appl. Phys. 23, 103 (1952). JAPIAU 0021-8979 10.1063/1.1701949
19. M. Lukovic and P. Grigolini, Power spectra for both interrupted and perennial aging processes, J. Chem. Phys. 129, 184102 (2008). JCPSA6 0021-9606 10.1063/1.3006051
20. P. Jung, Periodically driven stochastic systems, Phys. Rep. 234, 175 (1993). PRPLCM 0370-1573 10.1016/0370-1573(93)90022-6
21. E. Bertin and J. P. Bouchaud, Dynamical ultrametricity J. Phys. A: Math. Gen. 35, 3039 (2002). JPHAC5 0305-4470 10.1088/0305-4470/35/13/302
22. J. P. Bouchaud and D. S. Dean, Aging on Parisi's tree, J. Phys. I (France) 5, 265 (1995). JPGCE8 1155-4304 10.1051/jp1:1995127
23. G. Margolin and E. Barkai, Aging correlation functions for blinking nanocrystals, and other on-off stochastic processes, J. Chem. Phys. 121, 1566 (2004). JCPSA6 0021-9606 10.1063/1.1763136
24. A. Dechant, E. Lutz, D. A. Kessler, and E. Barkai, Superaging correlation function and ergodicity breaking for Brownian motion in logarithmic potentials, Phys. Rev. E 85, 051124 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.85.051124
25. D. A. Kessler and E. Barkai, Infinite Covariant Density for Diffusion in Logarithmic Potentials and Optical Lattices, Phys. Rev. Lett. 105, 120602 (2010). 10.1103/PhysRevLett.105.120602
26. L. Lizana, M. A. Lomholt, and T. Ambjörnsson, Single-file diffusion with non-thermal initial conditions, Physica A (Amsterdam) 395, 148 (2014). 10.1016/j.physa.2013.10.025
27. N. Leibovich and E. Barkai, Everlasting effect of initial conditions on single-file diffusion, Phys. Rev. E 88, 032107 (2013). PLEEE8 1539-3755 10.1103/PhysRevE.88.032107
28. A. Taloni, A. Chechkin, and J. Klafter, Generalized Elastic Model Yields a Fractional Langevin Description, Phys. Rev. Lett. 104, 160602 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.104.160602
29. A. G. Cherstvy, A. V. Chechkin, and R. Metzler, Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes, New J. Phys. 15, 083039 (2013). NJOPFM 1367-2630 10.1088/1367-2630/15/8/083039
30. F. Ionita and H. Meyer-Ortmanns, Physical Aging of Classical Oscillators, Phys. Rev. Lett. 112, 094101 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.094101
31. A. Bodrova, A. V. Chechkin, A. G. Cherstvy, and R. Metzler, Quantifying non-ergodic dynamics of force-free granular gases, Phys. Chem. Chem. Phys. 17, 21791 (2015). PPCPFQ 1463-9076 10.1039/C5CP02824H
32. E. Barkai, Aging in Subdiffusion Generated by a Deterministic Dynamical System, Phys. Rev. Lett. 90, 104101 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.90.104101
33. H. Kallabis and J. Krug, Persistence of Kardar-Parisi-Zhang interfaces, Europhys. Lett. 45, 20 (1999). EULEEJ 0295-5075 10.1209/epl/i1999-00125-0
34. K. A. Takeuchi and M. Sano, Evidence for geometry-dependentl universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence, J. Stat. Phys. 147, 853 (2012). JSTPBS 0022-4715 10.1007/s10955-012-0503-0
35. N. Leibovich and E. Barkai, Aging Wiener-Khinchin Theorem, Phys. Rev. Lett. 115, 080602 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.115.080602
36. A. Dechant and E. Lutz, Wiener-Khinchin Theorem for Nonstationary Scale-Invariant Processes, Phys. Rev. Lett. 115, 080603 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.115.080603
37. P. Dutta and P. M. Horn, Low-frequency fluctuations in solid: 1/f noise, Rev. Mod. Phys. 53, 497 (1981). RMPHAT 0034-6861 10.1103/RevModPhys.53.497
38. M. S. Keshner, 1/f noise, Proc. IEEE 70, 212 (1982). IEEPAD 0018-9219 10.1109/PROC.1982.12282
39. F. N. Hooge, T. G. M. Kleinpenning, and L. K. J. Vandamme, Experimental studies on 1/f noise, Rep. Prog. Phys. 44, 479 (1981). RPPHAG 0034-4885 10.1088/0034-4885/44/5/001
40. M. B. Weissman, 1/f noise and other slow, nonexponential kinetics in condensed matter, Rev. Mod. Phys. 60, 537 (1988). RMPHAT 0034-6861 10.1103/RevModPhys.60.537
41. A. C. Yadav, R. Ramaswamy, and D. Dhar, Power spectrum of mass and activity fluctuations in a sandpile, Phys. Rev. E 85, 061114 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.85.061114
42. M. Pelton, D. G. Grier, and P. Guyot-Sionnest, Characterizing quantum-dot blinking using noise power spectra, Appl. Phys. Lett. 85, 819 (2004). APPLAB 0003-6951 10.1063/1.1779356
43. P. A. Frantsuzov, S. Volkán-Kacsó, and B. Jankó, Universality of the fluorescence intermittency in nanoscale systems: Experiment and theory, Nano Lett. 13, 402 (2013). NALEFD 1530-6984 10.1021/nl3035674
44. D. Krapf, Nonergodicity in nanoscale electrodes, Phys. Chem. Chem. Phys. 15, 459 (2013). PPCPFQ 1463-9076 10.1039/C2CP42838E
45. O. G. Jensen, J. P Todoschuck, D. J. Crossley, and M. Gregotzki, Fractal linear models in geophysical models, in Nonlinear Variability in Geophysics, edited by D. Schertzer and S. Lovejoy, (Kluwer, Dordrecht, 1991).
46. B. B. Mandelbrot and J. R. Wallis, Some longrun properties of geophysical records, Water Resour. Res. 5, 321 (1969). WRERAQ 0043-1397 10.1029/WR005i002p00321
47. J. Banerjee, M. K. Verma, S. Manna, and S. Ghosh, Self-organized criticality and 1/f noise in single-channel current of voltage-dependent anion channel, Europhys. Lett. 73, 457 (2006). 10.1209/epl/i2005-10418-2
48. B. Kaulakys and M. Alaburda, Modeling scaled processes and 1/f noise using nonlinear stochastic differential equations, J. Stat. Mech. (2009) P02051. 10.1088/1742-5468/2009/02/P02051
49. B. B. Mandelbrot, Some noises with 1/f spectrum, a bridge between direct current and white noise, IEEE Trans. Inform. Theory 13, 289 (1967). IETTAW 0018-9448 10.1109/TIT.1967.1053992
50. T. Graves, R. B. Gramacy, N. Watkins, and C. L. E. Franzke, A brief history of long memory, arXiv:1406.6018v3.
51. G. Margolin and E. Barkai, Nonergodicity of a time series obeying Lévy statistics, J. Stat. Phys. 122, 137 (2006). JSTPBS 0022-4715 10.1007/s10955-005-8076-9
52. S. Sadegh, E. Barkai, and D. Krapf, Five critical exponents describing 1/f noise for intermittent quantum dots, New J. Phys. 16, 113054 (2014). NJOPFM 1367-2630 10.1088/1367-2630/16/11/113054
53. S. A. Diaz and M. Di Ventra, The role of measurement time on the universal crossover from 1/ f to non-1/ f noise behavior, J. Comput. Electron. 14, 203 (2015). 1569-8025 10.1007/s10825-014-0641-5
54. M. L. Boas, Mathematical Methods in the Physical Sciences (Wiley, Hoboken, NJ, 2006).
55. A. Dechant, E. Lutz, D. A. Kessler, and E. Barkai, Scaling Green-Kubo Relation and Application to Three Aging Systems, Phys. Rev. X 4, 011022 (2014). 10.1103/PhysRevX.4.011022
56. M. Abramowitz and I. A. Stegan, Handbook of Mathematical Functions (Dover, New York, 1972).
57. N. Leibovich and E. Barkai (unpublished).
58. K. A. Takeuchi (private communication).
59. F. Baumann and A. Gambassi, Ageing in the contact process: scaling behaviour and universal features, J. Stat. Mech. (2007) P01002. 10.1088/1742-5468/2007/01/P01002
60. K. A. Takeuchi, M. Kuroda, H. Chat, and M. Sano, Experimental realization of directed percolation criticality in turbulent liquid crystals, Phys. Rev. E 80, 051116 (2009). PLEEE8 1539-3755 10.1103/PhysRevE.80.051116
61. C. Godrèche and J. M. Luck, Response of non-equilibrium systems at criticality: ferromagnetic models in dimension two and above, J. Phys. A: Math. Gen. 33, 9141 (2000). JPHAC5 0305-4470 10.1088/0305-4470/33/50/302
62. J. M. Drouffe and C. Godrèche, Temporal correlations and persistence in the kinetic Ising model: the role of temperature, Eur. Phys. J. B 20, 281 (2001). EPJBFY 1434-6028 10.1007/s100510170277
63. P. Frantsuzov, M. Kuno, B. Janko, and R. A. Marcus, Universal emission intermittency in quantum dots, nanorods and nanowires, Nat. Phys. 4, 519 (2008). 1745-2473 10.1038/nphys1001
64. F. D. Stefani, J. P. Hoogenboom, and E. Barkai, Beyond quantum jumps: Blinking nanoscale light emitters, Phys. Today 62 (2), 34 (2009). PHTOAD 0031-9228 10.1063/1.3086100
65. G. Margolin and E. Barkai, Nonergodicity of Blinking Nanocrystals and Other Lévy-Walk Processes, Phys. Rev. Lett. 94, 080601 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.080601
66. M. Pelton, G. Smith, N. F. Scherer, and R. A. Marcus, Evidence for a diffusion-controlled mechanism for fluorescence blinking of colloidal quantum dots, Proc. Natl. Acad. Sci. USA 104, 14249 (2007). PNASA6 0027-8424 10.1073/pnas.0706164104
67. P. Manneville, Intermittency, self-similarity and 1/f spectrum in dissipative dynamical systems, J. Phys. 41, 1235 (1980). JOPQAG 0302-0738 10.1051/jphys:0198000410110123500
68. C. Godréche and J. M. Luck, Statistics of the occupation time of renewal processes, J. Stat. Phys. 104, 489 (2001). JSTPBS 0022-4715 10.1023/A:1010364003250
69. S. B. Lowen and M. C. Teich, Fractal renewal processes generate 1/f noise, Phys. Rev. E 47, 992 (1993). 1063-651X 10.1103/PhysRevE.47.992
70. T. E. Harris, Diffusion with "collisions" between particles, J. Appl. Probab. 2 (2), 323 (1965). 10.1017/S002190020010868X
71. P. L. Krapivsky, K. Mallick, and T. Sadhu, Large Deviations in Single-File Diffusion, Phys. Rev. Lett. 113, 078101 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.113.078101
72. C. Hegde, S. Sabhapandit, and A. Dhar, Universal Large Deviations for the Tagged Particle in Single-File Motion, Phys. Rev. Lett. 113, 120601 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.113.120601
73. A. L. Hodgkin and R. D. Keynes, The potassium permeability of a giant nerve fibre, J. Physiol. 128, 61 (1955). JPHYA7 0022-3751 10.1113/jphysiol.1955.sp005291
74. R. I. Macay and R. M. Oliver, The time dependence of single file diffusion, Biophys. J. 7, 545 (1967). BIOJAU 0006-3495 10.1016/S0006-3495(67)86605-0
75. K. Hahn, J. Karger, and V. Kukla, Single File Diffusion Observation, Phys. Rev. Lett. 76, 2762 (1996). PRLTAO 0031-9007 10.1103/PhysRevLett.76.2762
76. Q. H. Wei, C. Bechinger, and P. Leiderer, Single-File Diffusion of Colloids in One-Dimensional Channels, Science 287, 625 (2000). SCIEAS 0036-8075 10.1126/science.287.5453.625
77. C. Lutz, M. Kollmann, P. Leiderer, and C. Bechinger, Diffusion of colloids in one-dimensional light channels, J. Phys.: Condens. Matter 16, S4075 (2004). JCOMEL 0953-8984 10.1088/0953-8984/16/38/022
78. S. Marksteiner, K. Ellinger, and P. Zoller, Anomalous diffusion and Lévy walks in optical lattices, Phys. Rev. A 53, 3409 (1996). PLRAAN 1050-2947 10.1103/PhysRevA.53.3409
79. H. C. Fogedby and R. Metzler, DNA Bubble Dynamics as a Quantum Coulomb Problem, Phys. Rev. Lett. 98, 070601 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.98.070601
80. G. S. Manning, Limiting laws and counterion condensation in polyelectrolyte solutions I. Colligative properties, J. Chem. Phys. 51, 924 (1969). JCPSA6 0021-9606 10.1063/1.1672157
81. A. J. Bray, Random walks in logarithmic and power-law potentials, nonuniversal persistence, and vortex dynamics in the two-dimensional XY model, Phys. Rev. E 62, 103 (2000). 1063-651X 10.1103/PhysRevE.62.103
82. A. Dechant, E. Lutz, D. A. Kessler, and E. Barkai, Fluctuations of Time Averages for Langevin Dynamics in a Binding Force Field, Phys. Rev. Lett. 107, 240603 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.107.240603
83. M. Niemann, E. Barkai, and H. Kantz, Renewal theory for a system with internal states, Math. Model. Nat. Phenom. 11, 191 (2016). 0973-5348 10.1051/mmnp/201611312