Effective degrees of freedom of a random walk on a fractal

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Alexander S Balankin

Abstract

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν-dimensional space F^{ν} equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν) and fractal dimensionalities is deduced. The intrinsic time of random walk in F^{ν} is inferred. The Laplacian operator in F^{ν} is constructed. This allows us to map physical problems on fractals into the corresponding problems in F^{ν}. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

References

Oct 1, 1985·Physical Review A: General Physics·R A Guyer
Nov 1, 1985·Physical Review A: General Physics·B O'Shaughnessy, I Procaccia
Nov 15, 1990·Physical Review. a·A BundeH E Roman
Jun 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·H E Roman
Jan 15, 1991·Physical Review. B, Condensed Matter·X F He
Feb 4, 1985·Physical Review Letters·B O'Shaughnessy, I Procaccia
Feb 12, 1996·Physical Review Letters·R Burioni, D Cassi
Apr 17, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L Acedo, S B Yuste
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·C F Moukarzel
Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·L Acedo, S B Yuste
Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Gerald Paul, H Eugene Stanley
Apr 20, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Daniel CamposJoaquim Fort
Feb 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S Sellers, J A Barker
Oct 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander S BalankinDidier Samayoa Ochoa
Apr 28, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C P Haynes, A P Roberts
Aug 8, 2009·Physical Review Letters·Christophe P Haynes, Anthony P Roberts
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander S BalankinMiguel Angel Martínez Cruz
Mar 17, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Yasmine MerozJoseph Klafter
Mar 10, 2012·Physical Review Letters·Shlomi ReuveniRony Granek
Apr 3, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander S Balankin, Benjamin Espinoza Elizarraraz
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander S Balankin, Benjamin Espinoza Elizarraraz
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R M S FerreiraF A Oliveira
Dec 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander S BalankinDaniel Morales Matamoros
Feb 2, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Zongzheng ZhouRobert M Ziff
Feb 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Gianluca Calcagni
Jun 19, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander S BalankinClaudia L Martínez-González
Jul 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Federico BiancoAngelo Vulpiani
Oct 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander S BalankinViktor Tapia
Jul 1, 2014·Scientific Reports·N PoséH J Herrmann
Apr 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alexander S Balankin, Leonardo Flores-Cano
May 16, 2015·Physical Review Letters·M V TammA V Chertovich

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Citations

Dec 15, 2016·Physical Review. E·F D A Aarão Reis
Jul 2, 2018·Entropy·Alireza Khalili GolmankhanehDumitru Baleanu

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