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Article

Comb Model: Non-Markovian versus Markovian

1
Department of Physics, Technion-Israel Institute of Technology, Haifa 32000, Israel
2
Department of Physics, Universitat Autónoma de Barcelona, Bellaterra, 08193 Barcelona, Spain
3
Department of Chemistry, Southern Methodist University, Dallas, TX 75275-0314, USA
*
Author to whom correspondence should be addressed.
Fractal Fract. 2019, 3(4), 54; https://doi.org/10.3390/fractalfract3040054
Received: 22 October 2019 / Revised: 21 November 2019 / Accepted: 6 December 2019 / Published: 10 December 2019
(This article belongs to the Special Issue 2019 Selected Papers from Fractal Fract’s Editorial Board Members)
Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study two generalizations of comb models and present a generic method to obtain their transport properties. The first is a continuous time random walk on a many dimensional m + n comb, where m and n are the dimensions of the backbone and branches, respectively. We observe subdiffusion, ultra-slow diffusion and random localization as a function of n. The second deals with a quantum particle in the 1 + 1 comb. It turns out that the comb geometry leads to a power-law relaxation, described by a wave function in the framework of the Schrödinger equation. View Full-Text
Keywords: comb model; continuous time random walk; fractional Fokker-Planck equation; subdiffusion; Fox H-function; fractional Schrödinger equation comb model; continuous time random walk; fractional Fokker-Planck equation; subdiffusion; Fox H-function; fractional Schrödinger equation
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MDPI and ACS Style

Iomin, A.; Méndez, V.; Horsthemke, W. Comb Model: Non-Markovian versus Markovian. Fractal Fract. 2019, 3, 54. https://doi.org/10.3390/fractalfract3040054

AMA Style

Iomin A, Méndez V, Horsthemke W. Comb Model: Non-Markovian versus Markovian. Fractal and Fractional. 2019; 3(4):54. https://doi.org/10.3390/fractalfract3040054

Chicago/Turabian Style

Iomin, Alexander, Vicenç Méndez, and Werner Horsthemke. 2019. "Comb Model: Non-Markovian versus Markovian" Fractal and Fractional 3, no. 4: 54. https://doi.org/10.3390/fractalfract3040054

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