On the field dependence of random walks in the presence of random fields

A. Bunde; S. Havlin; H. E. Roman; G. Schildt; H. E. Stanley

doi:10.1007/BF01019166

On the field dependence of random walks in the presence of random fields

A. Bunde, S. Havlin, H. E. Roman, G. Schildt, H. E. Stanley

Department of Physics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Numerical simulations and scaling arguments are used to study the field dependence of a random walk in a one-dimensional system with a bias field on each site. The bias is taken randomly with equal probability to be +E or -E. The probability density -P(x, t) is found to scale asymptotically as {Mathematical expression} with A(E)=ln[(1+E)/(1-E)], β=4.25, and α=1.25. The mean square displacement scales as {Mathematical expression}, where F(u)∼ln⁴u asymptotically.

Original language	English
Pages (from-to)	1271-1276
Number of pages	6
Journal	Journal of Statistical Physics
Volume	50
Issue number	5-6
DOIs	https://doi.org/10.1007/BF01019166
State	Published - Mar 1988

Keywords

Random walks
anomalous diffusion
density distribution
fluctuations
random fields

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10.1007/BF01019166

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title = "On the field dependence of random walks in the presence of random fields",

abstract = "Numerical simulations and scaling arguments are used to study the field dependence of a random walk in a one-dimensional system with a bias field on each site. The bias is taken randomly with equal probability to be +E or -E. The probability density -P(x, t) is found to scale asymptotically as {Mathematical expression} with A(E)=ln[(1+E)/(1-E)], β=4.25, and α=1.25. The mean square displacement scales as {Mathematical expression}, where F(u)∼ln4u asymptotically.",

keywords = "Random walks, anomalous diffusion, density distribution, fluctuations, random fields",

author = "A. Bunde and S. Havlin and Roman, {H. E.} and G. Schildt and Stanley, {H. E.}",

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AU - Bunde, A.

AU - Havlin, S.

AU - Roman, H. E.

AU - Schildt, G.

AU - Stanley, H. E.

PY - 1988/3

Y1 - 1988/3

N2 - Numerical simulations and scaling arguments are used to study the field dependence of a random walk in a one-dimensional system with a bias field on each site. The bias is taken randomly with equal probability to be +E or -E. The probability density -P(x, t) is found to scale asymptotically as {Mathematical expression} with A(E)=ln[(1+E)/(1-E)], β=4.25, and α=1.25. The mean square displacement scales as {Mathematical expression}, where F(u)∼ln4u asymptotically.

AB - Numerical simulations and scaling arguments are used to study the field dependence of a random walk in a one-dimensional system with a bias field on each site. The bias is taken randomly with equal probability to be +E or -E. The probability density -P(x, t) is found to scale asymptotically as {Mathematical expression} with A(E)=ln[(1+E)/(1-E)], β=4.25, and α=1.25. The mean square displacement scales as {Mathematical expression}, where F(u)∼ln4u asymptotically.

KW - Random walks

KW - anomalous diffusion

KW - density distribution

KW - fluctuations

KW - random fields

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SN - 0022-4715

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SP - 1271

EP - 1276

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 5-6

ER -

On the field dependence of random walks in the presence of random fields

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Keywords

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