Equivalence of kinetic-theory and random-matrix approaches to Lyapunov spectra of hard-sphere systems

PHYSICA D-NONLINEAR PHENOMENA

卷:239

Article

de Wijn, Astrid S.^1,2,3 

[1] Radboud Univ Nijmegen, Inst Mol & Mat, NL-6525 AJ Nijmegen, Netherlands

[2] Univ Utrecht, Inst Theoret Phys, NL-3584 CE Utrecht, Netherlands

[3] Max Planck Inst Phys Komplexer Syst, D-01187 Dresden, Germany

关键词: Lyapunov exponents;    Lyapunov modes;    Goldstone modes;    Hard spheres;    High-dimensional chaos;    Random matrices;   

DOI  :  10.1016/j.physd.2010.06.007

来源: Elsevier

【 摘 要 】

In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute values exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical approaches to these exponents so far can be divided into two groups, macroscopically oriented approaches, using kinetic theory or hydrodynamics, and more microscopically oriented random-matrix approaches in quasi-one-dimensional systems. In this paper, I present an approach using random matrices and weak-disorder expansion in an arbitrary number of dimensions. Correlations between subsequent collisions of a particle are taken into account. It is shown that the results are identical to those of a previous approach based on an extended Enskog equation. I conclude that each approach has its merits, and provides different insights into the approximations made, which include the Stosszahlansatz, the continuum limit, and the long wavelength approximation. The comparison also gives insight into possible connections between Lyapunov exponents and fluctuations. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free