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

Felipe Barra RCH-UCSP-P Thomas Gilbert B-ULB-NP Mauricio Andrés Romo Jorquera RCH-UCSP-P

arXiv subject: Chaotic Dynamics (nlin.CD) mathscidoc:2205.80001

2006.1
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 in terms of the properties of the Pollicott-Ruelle resonance spectrum and the corresponding eigenvectors.
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@inproceedings{felipe2006drift,
  title={Drift of particles in self-similar systems and its Liouvillian interpretation},
  author={Felipe Barra, Thomas Gilbert, and Mauricio Andrés Romo Jorquera},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220526144942134152320},
  year={2006},
}
Felipe Barra, Thomas Gilbert, and Mauricio Andrés Romo Jorquera. Drift of particles in self-similar systems and its Liouvillian interpretation. 2006. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220526144942134152320.
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