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.
Original language | American English |
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Article number | 54 |
Pages (from-to) | 1-13 |
Number of pages | 13 |
Journal | Fractal and Fractional |
Volume | 3 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- Comb model
- Continuous time random walk
- Fox H-function
- Fractional Fokker-Planck equation
- Fractional Schrödinger equation
- Subdiffusion