Comb model: Non-markovian versus markovian

Alexander Iomin*, Vicenç Méndez, Werner Horsthemke

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

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 languageAmerican English
Article number54
Pages (from-to)1-13
Number of pages13
JournalFractal and Fractional
Volume3
Issue number4
DOIs
Publication statusPublished - 2019

Keywords

  • Comb model
  • Continuous time random walk
  • Fox H-function
  • Fractional Fokker-Planck equation
  • Fractional Schrödinger equation
  • Subdiffusion

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