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

We investigate the origin of diffusion in non-chaotic systems. As an example, we consider 1D 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...

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Bibliographic Details
Published in:Physica. D 2003-06, Vol.180 (3), p.129-139
Main Authors: Cecconi, Fabio, del-Castillo-Negrete, Diego, Falcioni, Massimo, Vulpiani, Angelo
Format: Article
Language:English
Subjects:
Chaos
Diffusion
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Summary:We investigate the origin of diffusion in non-chaotic systems. As an example, we consider 1D 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; (ii) a mechanism that suppresses periodic orbits.
ISSN:0167-2789
1872-8022
DOI:10.1016/S0167-2789(03)00051-4