Drift of particles in self-similar systems and its Liouvillian interpretation

Details Drift of particles in self-similar systems and its Liouvillian interpretation Drift of particles in self-similar systems and its Liouvillian interpretation

2006-01-19

arxiv.org/abs/nlin/0601042v1

Phys. Rev. E 73, 026211 (2006) [14 pages]

Nonlinear Sciences

Chaotic Dynamics

To appear in Phys. Rev. E

Scientific paper

10.1103/PhysRevE.73.026211

We study the dynamics of classical particles in different classes of spatially extended self-similar systems, consisting of (i) a self-similar Lorentz billiard channel, (ii) a self-similar graph, and (iii) a master equation. In all three systems the particles typically drift at constant velocity and spread ballistically. These transport properties are analyzed in terms of the spectral properties of the operator evolving the probability densities. For systems (i) and (ii), we explain the drift from the properties of the Pollicott-Ruelle resonance spectrum and corresponding eigenvectors

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