Chaotic features of molecular-dynamics systems

Everything that you see around us consists of moving atoms and molecules. Description of gases is founded on the Boltzmann equation which is, however, not applicable to the condensed matter. Only when the computers appeared in the National Laboratories in US their advanced scientists proceeded with modeling and simulation of dense systems of many particles interacting with each other. Classical systems were treated. The modeling was based on the numerical simulation of the Newton equations of motion with the simplest potentials of inter-particle interactions. Hundreds of particles were considered that time. Trillions are treated now with rather realistic interaction potentials. Despite (or because of) the lasting achievements of MMD, the chaos appearance in the system is not analyzed properly. It is the objective of our work. The theory of the method is presented and standards of requirements are derived for practical modeling & simulations.
Principle problems of classical method of molecular dynamics (MMD) are treated. The method was conceived for half a century ago as a computational tool for the solution of complex statistical physics problems. Now it is one of the most powerful numerical approaches in the condensed state theory. The method is based on the solution of the equations of motion for systems of many particles. Therefore MMD is directly connected with the basic conceptions of the classical statistical physics, in particular with the problem of the irreversibility origin. Dynamic and stochastic features of MD systems are analyzed, which are caused by numerical integration errors and the local Lyapunov instability of particles trajectories.