Scaling Green-Kubo relation and application to three aging systems

Physical Review X

Volumn 4, Issue 1, 2014, Pages

  Dechant, A ^a   Lutz, E ^a,b   Kessler, D A ^c   Barkai, E ^c  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^c BAR ILAN UNIVERSITY   (Israel)

Author keywords

Statistical physics

Indexed keywords

AGING OF MATERIALS; DIFFERENTIAL EQUATIONS; KINETIC THEORY OF GASES;

ANOMALOUS DIFFUSION; CORRELATION FUNCTION; DIFFERENT MECHANISMS; FRACTIONAL LANGEVIN EQUATIONS; GREEN-KUBO RELATIONS; POWER-LAW CORRELATIONS; STATISTICAL PHYSICS; VELOCITY AUTOCORRELATION FUNCTIONS;

DIFFUSION;

EID: 84900297669     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.4.011022     Document Type: Article

References (74)

1. E. Koscielny-Bunde, A. Bunde, S. Havlin, H. E. Roman, Y. Goldreich, and H.-J. Schellnhuber, Indication of a Universal Persistence Law Governing Atmospheric Variability, Phys. Rev. Lett. 81, 729 (1998).
2. F. Lillo and R. N. Mantegna, Power-Law Relaxation in a Complex System: Omori Law After a Financial Market Crash, Phys. Rev. E 68, 016119 (2003).
3. W. Min, G. Luo, B. J. Cherayil, S. C. Kou, and X. S. Xie, Observation of a Power-Law Memory Kernel for Fluctuations within a Single Protein Molecule, Phys. Rev. Lett. 94, 198302 (2005).
4. L. Silvestri, L. Fronzoni, P. Grigolini, and P. Allegrini, Event-Driven Power-Law Relaxation in Weak Turbulence, Phys. Rev. Lett. 102, 014502 (2009).
5. J.-P. Bouchaud, Weak Ergodicity Breaking and Aging in Disordered Systems, J. Phys. I France 2, 1705 (1992).
6. L. F. Cugliandolo, J. Kurchan, and G. Parisi, Off Equilibrium Dynamics and Aging in Unfrustrated Systems, J. Phys. I France 4, 1641 (1994).
7. G. Margolin and E. Barkai, Aging correlation functions for blinking nanocrystals, and other on-off stochastic processes, J. Chem. Phys. 121, 1566 (2004).
8. S. Burov, R. Metzler, and E. Barkai, Aging and Nonergodicity Beyond the Khinchin Theorem, Proc. Natl. Acad. Sci. U.S.A. 107, 13 228 (2010).
9. G. I. Taylor, Diffusion by Continuous Movements, Proc. London Math. Soc. s2-20, 196 (1922).
10. M. S. Green, Markoff Random Processes and the Statistical Mechanics of Time-Dependent Phenomena. II. Irreversible Processes in Fluids, J. Chem. Phys. 22, 398 (1954).
11. R. Kubo, Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems, J. Phys. Soc. Jpn. 12, 570 (1957).
12. G. Zumofen and J. Klafter, Power Spectra and Random Walks in Intermittent Chaotic Systems, Physica (Amsterdam) 69, 436 (1993).
13. Y. Castin, J. Dalibard, and C. Cohen-Tannoudji, The Limits of Sisyphus Cooling in Light Induced Kinetic Effects on Atoms, Ions and Molecules, edited by L. Moi, S. Gozzini, and C. Gabbanini (ETS Editrice, Pisa, 1991), p. 5.
14. S. Marksteiner, K. Ellinger, and P. Zoller, Anomalous Diffusion and Lévy Walks in Optical Lattices, Phys. Rev. A 53, 3409 (1996).
15. 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).
16. 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).
17. F. Bouchet and T. Dauxois, Prediction of Anomalous Diffusion and Algebraic Relaxations for Long-Range Interacting Systems, Using Classical Statistical Mechanics, Phys. Rev. E 72, 045103(R) (2005).
18. G. S. Manning, Limiting Laws and Counterion Condensation in Polyelectrolyte Solutions I. Colligative Properties, J. Chem. Phys. 51, 924 (1969).
19. A. E. Cohen, Control of Nanoparticles with Arbitrary Two-Dimensional Force Fields, Phys. Rev. Lett. 94, 118102 (2005).
20. P. H. Chavanis and R. Manella, Self-Gravitating Brownian Particles in Two Dimensions: The Case of N / 2 Particles, Eur. Phys. J. B 78, 139 (2010).
21. H. C. Fogedby and R. Metzler, DNA Bubble Dynamics as a Quantum Coulomb Problem, Phys. Rev. Lett. 98, 070601 (2007).
22. O. Hirschberg, D. Mukamel, and G. M. Schütz, Approach to Equilibrium of Diffusion in a Logarithmic Potential, Phys. Rev. E 84, 041111 (2011).
23. O. Hirschberg, D. Mukamel, and G. M. Schütz, Diffusion in a Logarithmic Potential: Scaling and Selection in the Approach to Equilibrium, J. Stat. Mech. (2012), P02001.
24. E. Lutz, Fractional Langevin Equation, Phys. Rev. E 64, 051106 (2001).
25. N. Pottier, Aging Properties of an Anomalously Diffusing Particule, Physica (Amsterdam) 317, 371 (2003).
26. M. Weiss, M. Elsner, F. Kartberg, and T. Nilsson, Anomalous Subdiffusion Is a Measure for Cytoplasmic Crowding in Living Cells, Biophys. J. 87, 3518 (2004).
27. M. Weiss, Single-Particle Tracking Data Reveal Anticorrelated Fractional Brownian Motion in Crowded Fluids, Phys. Rev. E 88, 010101(R) (2013).
28. L. Bruno, V. Levi, M. Brunstein, and M. A. Despósito, Transition to Superdiffusive Behavior in Intracellular Actin-Based Transport Mediated by Molecular Motors, Phys. Rev. E 80, 011912 (2009).
29. A. Dechant and E. Lutz, Connecting Active and Passive Microrheology in Living Cells, arXiv:1307.6466.
30. J.-P. Bouchaud and A. Georges, Anomalous Diffusion in Disordered Media: Statistical Mechanisms, Models and Physical Applications, Phys. Rep. 195, 127 (1990).
31. J. Klafter, A. Blumen, G. Zumofen, and M. F. Shlesinger, Lévy Walk Approach to Anomalous Diffusion, Physica (Amsterdam) 168, 637 (1990).
32. H. Scher and M. Lax, Stochastic Transport in a Disordered Solid. I. Theory, Phys. Rev. B 7, 4491 (1973).
33. H. Scher and E.W. Montroll, Anomalous Transit-Time Dispersion in Amorphous Solids, Phys. Rev. B 12, 2455 (1975).
34. C. Godrèche and J. M. Luck, Statistics of the Occupation Time of Renewal Processes, J. Stat. Phys. 104, 489 (2001).
35. E. Barkai and Y-C. Cheng, Aging Continuous Time Random Walks, J. Chem. Phys. 118, 6167 (2003).
36. M. F. Shlesinger, B. J. West, and J. Klafter, Lévy Dynamics of Enhanced Diffusion: Application to Turbulence, Phys. Rev. Lett. 58, 1100 (1987).
37. G. Ramos-Fernàndez, J. L. Mateos, O. Miramontes, G. Cocho, H. Larralde, and B. Ayala-Orozco, Lévy Walk Patterns in the Foraging Movements of Spider Monkeys (Ateles geoffroyi), Behav. Ecol. Sociobiol. 55, 223 (2004).
38. Y. J. Jung, E. Barkai, and R. J. Silbey, Lineshape Theory and Photon Counting Statistics for Blinking Quantum Dots: A Lévy Walk Process, Chem. Phys. 284, 181 (2002).
39. G. R. Kneller, Generalized Kubo Relations and Conditions for Anomalous Diffusion: Physical Insights from a Mathematical Theorem, J. Chem. Phys. 134, 224106 (2011).
40. J.-P. Bouchaud and D. S. Dean, Aging on Parisi's Tree, J. Phys. I France 5, 265 (1995).
41. P. Le Doussal, C. Monthus, and D. S. Fisher, Random Walkers in One-Dimensional Random Environments: Exact Renormalization Group Analysis, Phys. Rev. E 59, 4795 (1999).
42. B. Rinn, P. Maass, and J.-P. Bouchaud, Hopping in the Glass Configuration Space: Subaging and Generalized Scaling Laws, Phys. Rev. B 64, 104417 (2001).
43. C. Monthus, Anomalous Diffusion, Localization, Aging, and Subaging Effects in Trap Models at Very Low Temperature, Phys. Rev. E 68, 036114 (2003).
44. E. Lutz, Anomalous Diffusion and Tsallis Statistics in an Optical Lattice, Phys. Rev. A 67, 051402 (2003).
45. P. Douglas, S. Bergamini, and F. Renzoni, Tunable Tsallis Distributions in Dissipative Optical Lattices, Phys. Rev. Lett. 96, 110601 (2006).
46. H. Katori, S. Schlipf, and H. Walther, Anomalous Dynamics of a Single Ion in an Optical Lattice, Phys. Rev. Lett. 79, 2221 (1997).
47. D. A. Kessler and E. Barkai, Infinite Covariant Density for Diffusion in Logarithmic Potentials and Optical Lattices, Phys. Rev. Lett. 105, 120602 (2010).
48. 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).
49. D. A. Kessler and E. Barkai, Theory of Fractional Lévy Kinetics for Cold Atoms Diffusing in Optical Lattices, Phys. Rev. Lett. 108, 230602 (2012).
50. G. Falkovich, K. Gawedzki, and M. Vergassola, Particles and Fields in Fluid Turbulence, Rev. Mod. Phys. 73, 913 (2001).
51. J. Duplat, S. Kheifets, T. Li, M. G. Raizen, and E. Villermaux, Superdiffusive Trajectories in Brownian Motion, Phys. Rev. E 87, 020105 (2013).
52. A. Dechant and E. Lutz, Anomalous Spatial Diffusion and Multifractality in Optical Lattices, Phys. Rev. Lett. 108, 230601 (2012).
53. L. Perotti, V. Alekeseev, and H. Walther, Transport of a Single Ion in an Optical Lattice: Spatial Diffusion and Energy, Opt. Commun. 183, 73 (2000).
54. B. B. Mandelbrot and J.W. Van Ness, Fractional Brownian Motions, Fractional Noises and Applications, SIAM Rev. 10, 422 (1968).
55. I. Goychuk, and P. Hänggi, Anomalous Escape Governed by Thermal 1/f Noise, Phys. Rev. Lett. 99, 200601 (2007).
56. S. Burov and E. Barkai, Critical Exponent of the Fractional Langevin Equation, Phys. Rev. Lett. 100, 070601 (2008).
57. A. Taloni, A. Chechkin, and J. Klafter, Generalized Elastic Model Yields a Fractional Langevin Equation Description, Phys. Rev. Lett. 104, 160602 (2010).
58. L. Lizana, T. Ambjörnsson, A. Taloni, E. Barkai, and M. A. Lomholt, Foundation of Fractional Langevin Equation: Harmonization of a Many-Body Problem, Phys. Rev. E 81, 051118 (2010).
59. I. M. Sokolov, Models of Anomalous Diffusion in Crowded Environments, Soft Matter 8, 9043 (2012).
60. F. Gallet, D. Arcizet, P. Bohec, and A. Richert, Power Spectrum of Out-of-Equilibrium Forces in Living Cells: Amplitude and Frequency Dependence, Soft Matter 5, 2947 (2009).
61. X. Trepat, G. Lenormand, and J. J. Fredberg, Universality in Cell Mechanics, Soft Matter 4, 1750 (2008).
62. For λ < 1, the noise process corresponds to fractional Gaussian noise in the long-time limit, whereas for λ > 1, it is identical to Riemann-Liouville fractional Brownian motion with the Hurst exponent H = (λ -1)/2.
63. M. Kuno, D. P. Fromm, H. F. Hamann, A. Gallagher, and D. J. Nesbitt, Nonexponential Blinking Kinetics of Single CdSe Quantum Dots: A Universal Power Law Behavior, J. Chem. Phys. 112, 3117 (2000).
64. M. Kuno, D. P. Fromm, H. F. Hamann, A. Gallagher, and D. J. Nesbitt, On/Off Fluorescence Intermittency of Single Semiconductor Quantum Dots, J. Chem. Phys. 115, 1028 (2001).
65. K. T. Shimizu, R. G. Neuhauser, C. A. Leatherdale, S. A. Empedocles, W. K. Woo, and M. G. Bawendi, Blinking Statistics in Single Semiconductor Nanocrystal Quantum Dots, Phys. Rev. B 63, 205316 (2001).
66. X. Brokmann, J.-P. Hermier, G. Messin, P. Desbiolles, J.-P. Bouchaud, and M. Dahan, Statistical Aging and Nonergodicity in the Fluorescence of Single Nanocrystals, Phys. Rev. Lett. 90, 120601 (2003).
67. J. Klafter, M. F. Shlesinger, and G. Zumofen, Beyond Brownian Motion, Phys. Today 49, 33 (1996).
68. G. Margolin, V. Protasenko, M. Kuno, and E. Barkai, Photon Counting Statistics for Blinking CdSe-ZnS Quantum Dots: A Lévy Walk Process, J. Phys. Chem. B 110, 19053 (2006).
69. J. J. Peterson and D. J. Nesbitt, Modified Power Law Behavior in Quantum Dot Blinking: A Novel Role for Biexcitons and Auger Ionization, Nano Lett. 9, 338 (2009).
70. N. Leibovich and E. Barkai, Everlasting Effect of Initial Conditions on Single-File Diffusion, Phys. Rev. E 88, 032107 (2013).
71. D. Froemberg and E. Barkai, Random Time Averaged Diffusivities for Lévy Walks, Eur. Phys. J. B 86, 331 (2013).
72. A. Godec and R. Metzler, Finite-Time Effects and Ultraweak Ergodicity Breaking in Superdiffusive Dynamics, Phys. Rev. Lett. 110, 020603 (2013).
73. J. Kursawe, J. Schulz, and R. Metzler, Transient Aging in Fractional Brownian and Langevin Equation Motion, Phys. Rev. E 88, 062124 (2013).
74. D. Froemberg and E. Barkai, Time-Averaged Einstein Relation and Fluctuating Diffusivities for the Lévy Walk, Phys. Rev. E 87, 030104(R) (2013).