Lyapunov exponent of dilute gas, liquid and solid plasmas

The Lyapunov exponent has been investigated both numerically and analytical ly for various plasma states. With the use of a three-dimensional particle code that calculates Coulomb forces among individual particles, instantaneo us expansion rates of nearby trajectories in a phase space are studied. It is found that the Lyapunov exponent has different dependences on the Coulom b coupling constant corresponding to dilute, liquid and solid plasmas. An a nalytical model is also developed and it gives a relation between the Lyapu nov exponent and the dielectric response function. The model indicates that the Lyapunov exponent is of the order of the plasma frequency in a dilute plasma, which agrees with simulation results. In a dilute plasma, large flu ctuation of the instantaneous expansion rate is shown to be caused by a clo se encounter which breaks the symmetry of force and leads to trajectory ins tability.