Local Einstein relation for fractals

Abstract We study single random walks and the electrical resistance for fractals obtained as the limit of a sequence of periodic structures. In the long-scale regime, power laws describe both the mean-square displacement of a random walk as a function of time and the electrical resistance as a funct...

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Bibliographic Details
Published inPhysica scripta Vol. 98; no. 9; pp. 95008 - 95015
Main Authors Padilla, L, Iguain, J L
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.09.2023
Subjects
Einstein relation
fractals
Power-law behaviours
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Summary:Abstract We study single random walks and the electrical resistance for fractals obtained as the limit of a sequence of periodic structures. In the long-scale regime, power laws describe both the mean-square displacement of a random walk as a function of time and the electrical resistance as a function of length. We show that the corresponding power-law exponents satisfy the Einstein relation. For shorter scales, where these exponents depend on length, we find how the Einstein relation can be generalized to hold locally. All these findings were analytically derived and confirmed by numerical simulations.
Bibliography:PHYSSCR-121124.R1
ISSN:0031-8949
1402-4896
DOI:10.1088/1402-4896/aceb3a