Chaotic scattering theory, thermodynamic formalism, and transport coefficients.
Chaotic scattering theory, thermodynamic formalism, and transport coefficients.
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混沌散射理论、热力学形式主义和传输系数。
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
J. Dorfman
中科院分区：
文献类型：
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作者：
P. Gaspard;J. Dorfman
本文详细讨论了经典多体系统输运和反应速率系数的混沌散射理论的基础。西奈，Ruelle，和Bowen的热力学形式论[D]。采用Ruelle，热力学形式（Addison-Wesley, Reading， MA, 1978）]，首次得到了系统相空间轨迹离开相空间有限区域的逃逸率表达式。这个表达式将逃逸率与永远被困在有限区域的分形相空间轨迹集的正Lyapunov指数和Kolmogorov-Sinai熵之和之间的差联系起来。这种关系在几个自由度的系统中是众所周知的，在这里我们把它推广到多个自由度的系统。该形式被应用于光滑双曲系统、元胞自动机晶格气体和硬球系统。在最后一种情况下，西奈的几何结构和同事[俄罗斯。数学。《生存》25,137 (1970)；42,181(1987)]用于描述台球系统的相关混沌散射现象。本文还讨论了这种形式在非双曲系统中的一些应用。
The foundations of the chaotic scattering theory for transport and reaction-rate coefficients for classical many-body systems are considered here in some detail. The thermodynamic formalism of Sinai, Ruelle, and Bowen [D. Ruelle, Thermodynamic Formalism (Addison-Wesley, Reading, MA, 1978)] is employed to obtain an expression for the escape rate for a phase-space trajectory of a system to leave a finite region of phase space for the first time. This expression relates the escape rate to the difference between the sum of the positive Lyapunov exponents and the Kolmogorov-Sinai entropy for the fractal set of phase-space trajectories that are trapped forever in the finite region. This relation is well known for systems of a few degrees of freedom and is extended here to systems with many degrees of freedom. The formalism is applied to smooth hyperbolic systems, to cellular-automata lattice gases, and to hard-sphere systems. In the last case, the geometric constructions of Sinai and co-workers [Russ. Math. Surv. 25, 137 (1970); 42, 181 (1987)] for billiard systems are used to describe the relevant chaotic scattering phenomena. Some applications of this formalism to nonhyperbolic systems are also discussed.