Stochastic properties of strongly coupled plasmas

Abstract

Stochastic properties of equilibrium strongly coupled plasmas are investigated by a molecular dynamics method. The Krylov-Kolmogorov entropy K and the dynamical memory time t(m) are calculated both for electrons and ions with mass ratios 10-10(5). Two values of K entropy for ions are discovered corresponding to electron and ion time scales. The dependence of the K entropy on the number of particles, the nonideality parameter, and the form of the interaction potential is investigated. The problem of the accuracy of molecular dynamics simulations is discussed. A universal relation between Kt(m) and the fluctuation of the total energy of the system is obtained. The relation does not depend on the numerical integration scheme, temperature, density, and the interparticle interaction potential, so that it may be applied to arbitrary dynamic systems. Transition from dynamic to stochastic correlation is treated for both electron and ion velocity autocorrelation functions, for Langmuir and ion-sound plasma wave dynamic structure factors. We point to quantum uncertainty as a physical reason which limits dynamic (Newton) correlation for times greater than t(m).

Stochastic and dynamic properties of molecular dynamics systems: Simple liquids, plasma and electrolytes, polymers

“…Set (1) is exponentially unstable for a system of more than two particles (e.g., see [3][4][5][6][7][8][9][10][11][12][13][14][15][16]). The parameter that determines the degree of instability, that is, the rate of divergence of initially close phase trajectories, is the averaged Lyapunov exponent or K-entropy K. It can be determined in several ways.…”

“…The values of t m are calculated at the same t value and different t values of t/2, t/5, t/10, etc. The limiting value of t m when t / t → 0 is the dynamical memory time t m for a given system and the selected numerical integration step t [14,15].…”

Standard of Molecular Dynamics Modeling and Simulation of Relaxation in Dense Media

“…Due to this instability there appears a dynamic memory time t m which limits the time interval when the Caushy problem is valid for MD numerical integration. For times greater than t m MD trajectory "forgets" its initial conditions and ceases to correlate with the hypothetical Newtonian trajectory with the same initial conditions [11,12]. We expect that the duration of ensemble-dependent part of the relaxation correlates with t m .…”

“…The number of ions in present simulations is N = 64-800. The choice of N and another details of simulations are discussed elsewhere [4,11].…”

“…However the time of the stochastization or dynamical memory time t m in nonideal plasma becomes greater than the time between collisions [11].…”