Superdiffusion in decoupled continuous time random walks

被引：13

作者：

Budde, C ^{[1
]}

Prato, D ^{[1
]}

Ré, M ^{[1
]}

机构：

[1] Univ Nacl Cordoba, Fac Matemat Astron & Fis, RA-5010 Cordoba, Argentina

来源：

PHYSICS LETTERS A | 2001年 / 283卷 / 5-6期

关键词：

D O I：

10.1016/S0375-9601(01)00234-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Continuous time random walk models with decoupled waiting time density are studied. When the spatial one-jump probability density belongs to the Levy distribution type and the total time transition is exponential a generalized superdiffusive regime is established. This is verified by showing that the square width of the probability distribution (appropriately defined) grows as t(2/gamma) with 0 < gamma less than or equal to 2 when t --> infinity. An important connection of our results and those of Tsallis' nonextensive statistics is shown. The normalized q-expectation value of x(2) calculated with the corresponding probability distribution behaves exactly as t(2/gamma) in the asymptotic limit. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：309 / 312

页数：4

共 19 条

[1]

ALEXANDER S, 1982, J PHYS LETT-PARIS, V43, pL625, DOI 10.1051/jphyslet:019820043017062500

[2]

BATCHELOR GK, 1926, P R SOC LONDON SER A, V110, P709

[3] TRANSPORT ASPECTS IN ANOMALOUS DIFFUSION - LEVY WALKS [J].

BLUMEN, A ;

ZUMOFEN, G ;

KLAFTER, J .

PHYSICAL REVIEW A, 1989, 40 (07) :3964-3974

[4] UNIFIED THEORY OF RELATIVE TURBULENT-DIFFUSION [J].

GROSSMANN, S ;

PROCACCIA, I .

PHYSICAL REVIEW A, 1984, 29 (03) :1358-1365

[5] STOCHASTIC PATHWAY TO ANOMALOUS DIFFUSION [J].

KLAFTER, J ;

BLUMEN, A ;

SHLESINGER, MF .

PHYSICAL REVIEW A, 1987, 35 (07) :3081-3085

[6]

Monin A. N., 1971, Statistical Fluid Mechanics, VII

[7]

Monin AS, 1971, STAT FLUID MECH, V1

[8]

MONTROLL E, 1979, FLUCTUATION PHENOMEN

[9] RANDOM WALKS ON LATTICES .2. [J].

MONTROLL, EW ;

WEISS, GH .

JOURNAL OF MATHEMATICAL PHYSICS, 1965, 6 (02) :167-+

[10] ANOMALOUS DIFFUSION IN LIVING POLYMERS - A GENUINE LEVY FLIGHT [J].

OTT, A ;

BOUCHAUD, JP ;

LANGEVIN, D ;

URBACH, W .

PHYSICAL REVIEW LETTERS, 1990, 65 (17) :2201-2204

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