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The origin of diffusion: the case of non chaotic systems

Fabio Cecconi·Diego del-Castillo-Negrete·Massimo Falcioni·Angelo Vulpiani
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Abstract

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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Fabio Cecconi, Diego del-Castillo-Negrete, Massimo Falcioni, Angelo Vulpiani. 2002-10-21. The origin of diffusion: the case of non chaotic systems. https://doi.org/10.1016/s0167-2789(03)00051-4

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