Classical dynamics on graphs

Details Classical dynamics on graphs Classical dynamics on graphs

2000-11-23

arxiv.org/abs/nlin/0011045v2

Nonlinear Sciences

Chaotic Dynamics

42 pages and 8 figures

Scientific paper

10.1103/PhysRevE.63.066215

We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator which generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms which decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs which converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system which undergoes a diffusion process before it escapes.

Affiliated with

Also associated with

No associations

Rating

Classical dynamics on graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classical dynamics on graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classical dynamics on graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-729600