PARTICLE SIMULATION OF LYAPUNOV EXPONENTS IN ONE-COMPONENT STRONGLY COUPLED PLASMAS

The Lyapunov exponents and instantaneous expansion rates in a phase sp ace of Coulomb many-body systems are measured with the use of a three- dimensional particle code SCOPE [K. Nishihara, Kakuyugo Kenkyu 66, 253 (1991)]. The code calculates particle dynamics determined by Coulomb forces among individual particles. The Lyapunov exponents normalized b y plasma frequency are found to be proportional to Gamma(-25) in the r ange of 1 less than or equal to Gamma less than or equal to 160, where Gamma is the Coulomb coupling constant of the ion one-component plasm a. There is a large jump of the Lyapunov exponent near Gamma similar t o 170, which corresponds to the phase transition from the liquid to th e solid state in the one-component plasma. In the solid state, the nor malized Lyapunov exponents are proportional to Gamma(-6/5) for 170<Gam ma<300. The observed dependence is discussed in analogy to a rigid-bod y particle system and a weakly nonlinear lattice system for liquid and solid states, respectively. Diffusion coefficients are found to be pr oportional to the third power of the Lyapunov exponent in the liquid s tate, that is, for 1 less than or equal to Gamma less than or equal to 160. These results imply that the Lyapunov exponent is in close relat ion to the transport processes. The instantaneous expansion rate start s from a small value and increases rapidly to a large peak value befor e declining slowly towards an asymptotic value. This stage is called t he Lyapunov transient stage. Products of the transient time and the Ly apunov exponent are found to be 1.5-2. Information of the initial stat e is lost after-the transient time. The chaotic behavior of the instan taneous expansion rate is also shown.