Complete spectrum of stochastic master equation for random walks on treelike fractals

Details Complete spectrum of stochastic master equation for random walks on treelike fractals Complete spectrum of stochastic master equation for random walks on treelike fractals

2011-10-20

arxiv.org/abs/1110.4459v1

EPL (Europhysics Letters), 2011, 96:40009

Physics

Condensed Matter

Statistical Mechanics

Definitive version accepted for publication in EPL (Europhysics Letters)

Scientific paper

10.1209/0295-5075/96/40009

We study random walks on a family of treelike regular fractals with a trap fixed on a central node. We obtain all the eigenvalues and their corresponding multiplicities for the associated stochastic master equation, with the eigenvalues being provided through an explicit recursive relation. We also evaluate the smallest eigenvalue and show that its reciprocal is approximately equal to the mean trapping time. We expect that our technique can also be adapted to other regular fractals with treelike structures.

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