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

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• 作者：Cecconi ; Fabio ; del-Castillo-Negrete ; Diego ; Falcioni ; Massimo ; Vulpiani ; Angelo
• 关键词：05.45.&minus ; a ; 05.60.&minus ; k ; Diffusion ; Chaos
• 刊名：Physica D
• 出版年：2003
• 出版时间：June 15, 2003
• 年：2003
• 卷：180
• 期：3-4
• 页码：129-139
• 全文大小：204 K

文摘

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.