Particle simulation of Lyapunov exponents in one-component strongly coupled plasmas

Abstract

The Lyapunov exponents and instantaneous expansion rates in a phase space 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 by plasma frequency are found to be proportional to ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}2\mathrm{/}5}$ in the range of 1\ensuremath{\leqslant}\ensuremath{\Gamma}\ensuremath{\leqslant}160, where \ensuremath{\Gamma} is the Coulomb coupling constant of the ion one-component plasma. There is a large jump of the Lyapunov exponent near \ensuremath{\Gamma}\ensuremath{\sim}170, which corresponds to the phase transition from the liquid to the solid state in the one-component plasma. In the solid state, the normalized Lyapunov exponents are proportional to ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}6\mathrm{/}5}$ for 170300. The observed dependence is discussed in analogy to a rigid-body particle system and a weakly nonlinear lattice system for liquid and solid states, respectively. Diffusion coefficients are found to be proportional to the third power of the Lyapunov exponent in the liquid state, that is, for 1\ensuremath{\leqslant}\ensuremath{\Gamma}\ensuremath{\leqslant}160. These results imply that the Lyapunov exponent is in close relation to the transport processes. The instantaneous expansion rate starts from a small value and increases rapidly to a large peak value before declining slowly towards an asymptotic value. This stage is called the Lyapunov transient stage. Products of the transient time and the Lyapunov exponent are found to be 1.5--2. Information of the initial state is lost after the transient time. The chaotic behavior of the instantaneous expansion rate is also shown.