Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1995-04-25
Nonlinear Sciences
Chaotic Dynamics
35 pages, compressed file, follow directions in header for ps file. Figures are available on request from jrd@glue.umd.edu
Scientific paper
10.1103/PhysRevE.52.3525
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, Bowen, and Ruelle is employed to obtain an expression for the escape-rate for a phase space trajectory to leave a finite open 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 K-S entropy for the fractal set of trajectories which are trapped forever in the open region. This result is well known for systems of a few degrees of freedom and is here extended to systems of many degrees of freedom. The formalism is applied to smooth hyperbolic systems, to cellular-automata lattice gases, and to hard sphere sytems. In the latter case, the goemetric constructions of Sinai {\it et al} for billiard systems are used to describe the relevant chaotic scattering phenomena. Some applications of this formalism to non-hyperbolic systems are also discussed.
Dorfman Robert J.
Gaspard Pierre
Парфенов Г. П.
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