Loss of dynamic memory in strongly coupled plasmas. Analytic evaluation of the time interval

Abstract
Broadening of a micro-particle wave packet makes its size close to the range of scattering potential. Diffraction increases uncertainty of a center of mass position to the value comparable with interparticle distance just after several collisions. Besides a single initial amplitude maximum splits in increasing numbers of local maxima at the particle motion. The character of particle motion changes drastically compared with Newton picture even in the systems of heavy atoms or molecules at normal and elevated temperatures to say nothing of plasma. The quantum broadening and uncertainty are triggers for exponential Lyapunov instability. The equation of motion were obtained for the system of N interacting particles which differs from Newtonian ones by appearance of stochastic terms. The trajectory divergence is defined by quantum diffusion at small times and then by exponential instability. The values of the memory loss time turn out to be relatively not large compared with inverse plasma frequency. The result corresponds to the importance of quantum effects in statistical thermodynamics of non-degenerate nonideal plasmas.