Comb model : Non-markovian versus markovian
Iomin, Alexander (Technion - Israel Institute of Technology. Department of Physics)
Méndez López, Vicenç (Universitat Autònoma de Barcelona. Departament de Física)
Horsthemke, Werner (Southern Methodist University. Department of Chemistry)

Date:	2019
Abstract:	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.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Comb model ; Continuous time random walk ; Fractional Fokker-Planck equation ; Subdiffusion ; Fox H-function ; Fractional Schrödinger equation
Published in:	Fractal and Fractional, Vol. 3, Issue 4 (December 2019) , art. 54, ISSN 2504-3110

DOI: 10.3390/fractalfract3040054

13 p, 351.5 KB

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