| Original Articles |
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Stretched Exponential Relaxation in Disordered Complex Systems: Fractal Time Random Walk Model |
| Ekrem Aydiner |
| Department of Physics, Dokuz Eylul University, Tr-35160 Izmir, Turkey |
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| Cite this article: |
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Ekrem Aydiner 2007 Chin. Phys. Lett. 24 1486-1490 |
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Abstract We have analytically derived the relaxation function for one-dimensional
disordered complex systems in terms of autocorrelation function of fractal time random walk by using operator formalism. We have shown that the relaxation function has stretched exponential, i.e. the Kohlrausch--Williams--Watts character for a fractal time random walk process.
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| Keywords:
05.40.-a
02.50.-r
02.30.-f
76.20.+q
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Received: 15 January 2007
Published: 17 May 2007
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| PACS: |
05.40.-a
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(Fluctuation phenomena, random processes, noise, and Brownian motion)
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02.50.-r
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(Probability theory, stochastic processes, and statistics)
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02.30.-f
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(Function theory, analysis)
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76.20.+q
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(General theory of resonances and relaxations)
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[1] Phillips J C 1996 Rep. Prog. Phys. 59 1133
[2] Chamberlin R W, Mozurkewich G and Orbach R 1984 Phys. Rev.Lett. 52 867 Hoogerbeets R, Orbach R and Luo W L 1985 Phys. Rev. Lett. 55 111 van Hemmen J L and Nieuwenhuys G J 1986 Europhys. Lett. 2 797 Nordblad P, Svedlindh P, Lundgren P and Sandlund L 2000 Phys.Rev. B 77 2391 Gunnarsson K, Svedlindh P, Nordblad P, Lundgren L, Aruga H andIto A 1988 Phys. Rev. Lett. 61 754
[3] Campbell I A 1985 J. Phys. Lett. 46 L1159
[4] Campbell I A, Flesselles J M, Jullien R and Botet R 1987 J.Phys. C: Solid State Phys. 20 L47 Campbell I A, Flesselles J M, Jullien R and Botet R 1988 Phys.Rev. B 37 3825 Lemke N and Campbell I A 1996 Physica A 230 554 de Almeida R M C, Lemke N, Pund P, Jullien R, Campbell I A andBertrand D 2001 J. Non Cryst. Solids 287 201 de Almeida R M C, Lemke N, Campbell I A 2001 J. Magn. Magn.Matter 226-230 1296 Jund P, Jullien R and Campbell I A 2001 Phys. Rev. E 63 036131 de Almeida R M C and Campbell I A 2000 Eur. Phys. J. B 18 513
[5] Palmer R G, Stein D L, Abrahams E and Anderson P W 1984 Phys.Rev. Lett. 53 958
[6] Khang B 1991 Phys. Rev. A 43 1791
[7] Dzugutov M and Philips J 1995 J. Non-Cryst. Solids 192-193 397
[8] Donsker M and Varadhan S 1975 Commun. Pure Appl. Math. 28 525 Donsker M and Varadhan S 1979 Commun. Pure Appl. Math. 32 721
[9] Grassberger P and Procaccia I 1982 J. Chem. Phys. 77 6281
[10] Barkema G, Biswas P and van Beijeren H 2001 Phys. Rev.Lett. 87 170601
[11] Rasaiah J C, Zhu J, Hubbard J B and Rubin R J 1990 J. Chem.Phys. 93 5768
[12] Roy M and Amritkar R E 1997 Phys. Rev. E 55 2422
[13] Frisch U and Sornette D 1997 J. Phys. I 7 1155
[14] Gamba A and Kolokolov I 1997 J. Stat. Phys. 94 759
[15] Gielis G and Maes C 1995 Europhys. Lett. 31 1
[16] Garrahan J P and Chandler D 2002 Phys. Rev. Lett. 89 035704
[17] Abrahams E 2005 Phys. Rev. E 71 051901
[18] Perez-Madrid A 2004 Phys. Rev. E 69 062102
[19] Aydiner E 2005 Phys. Rev. E 71 046103
[20] Kalmykov Y P 2004 Phys. Rev. E 70 051106
[21] Coffey W T, Kalmykov Y P and Titov S V 2003 Phys. Rev.E 67 061115
[22] Kalmykov Y P, Coffey W T, Crothers D S F and Titov S V 2004 Phys. Rev. E 70 041103
[23] Coffey W T, Kalmykov Y P and Titov S V 2002 J. Chem.Phys. 116 6422
[24] Aydiner A and Kiymac K 2004 Int. J. Mod. Phys. C 15 163
[25] Yoshioka S, Aso Y and Kojima S 2001 Pharm. Res. 13 256
[26] Fatkullin I, Kladko K, Mitkov I and Bishop A R 2001 Phys.Rev. E 63 067102
[27] D\'{\iaz-S\'{anchez A and P\'{erez-Garrido A 2001 Eur.Phys. J. B 24 483
[28] Simdyankin S I and Mousseau N 2003 Phys. Rev. E 68 041110
[29] Gomi S and Yonezawa F 1995 Phys. Rev. Lett. 74 4125
[30] Kohlrausch R 1847 Ann. Phys. (Leipzig) 12 393
[31] Williams G and Watts D C 1970 Trans. Faraday Soc. 66 80
[32] Hilfer R 2002 Phys. Rev. E 65 061510
[33] Hilfer R 1995 Fractals 3 211
[34] Hilfer R and Anton L 1995 Phys. Rev. E 51 R848
[35] Metzler R and Klafter J 2001 Adv. Chem. Phys. 116 223 Metzler R and Klafter J 2000 Phys. Rep. 339 1 Metzler R and Klafter J 2000 J. Non-Cryst. Sol. 305 81
[36] Montroll E W and Weiss G H 1965 J. Math. Phys. 6 167
[37] Scher H and Lax M 1973 Phys. Rev. B 7 4491
[38] Shlesinger M F and Montroll E W 1984 Proc. Natl. Acad.Sci. USA 81 1280
[39] Sher H and Montroll E W 1975 Phys. Rev. B 12 2455
[40] van Kampen N G 1981 Stochastic Processes inPhysics and Chemistry (Amsterdam: North-Holland)
[41] Hughes B D 1995 Random Walks and Random Environments(Oxford: Clarendon) vol 1
[42] Dattagupta S 1987 Relaxation Phenomena in CondensedMatter Physics (Orlando, FL: Academic)
[43] Aydiner E 2006 Chin. Phys. Lett. 23 3353
[44] Oldham K B and Spanier J 1974 The Fractional Calculus(New York: Academic)
[45] Erdelyi A 1954 Tables of Integral Transforms (New York:McGraw-Hill) |
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