The origin of diffusion: the case of non chaotic systems

Details The origin of diffusion: the case of non chaotic systems The origin of diffusion: the case of non chaotic systems

2002-10-21

arxiv.org/abs/nlin/0210049v2

Physica D, vol.180, pag.129-139, (2003)

Nonlinear Sciences

Chaotic Dynamics

RevTeX, 9 pages, 10 eps Figures

Scientific paper

We investigate the origin of diffusion in non-chaotic systems. As an example, we consider 1-$d$ map models whose slope is everywhere 1 (therefore the Lyapunov exponent is zero) but with random quenched discontinuities and quasi-periodic forcing. The models are constructed as non-chaotic approximations of chaotic maps showing deterministic diffusion, and represent one-dimensional versions of a Lorentz gas with polygonal obstacles (e.g., the Ehrenfest wind tree model). In particular, a simple construction shows that these maps define non-chaotic billiards in space-time. The models exhibit, in a wide range of the parameters, the same diffusive behavior of the corresponding chaotic versions. We present evidence of two sufficient ingredients for diffusive behavior in one-dimensional, non-chaotic systems: i) a finite-size, algebraic instability mechanism, and ii) a mechanism that suppresses periodic orbits.

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