The Motion of a Tracer Particle in a One-dimensional System: Analysis and Simulation
نویسنده
چکیده
Our goal is to obtain a test system for the evaluation of time-stepping methods in molecular dynamics. We consider a family of deterministic systems consisting of a finite number of particles interacting on a compact interval. The particles are given random initial conditions and interact through instantaneous energyand momentum-conserving collisions. As the number of particles, the particle density, and the mean particle speed go to infinity, the trajectory of a tracer particle is shown to converge to a stationary Gaussian process. We simulate the system with two numerical methods, one symplectic, the other energy-conserving, and assess the methods’ ability to recapture the system’s limiting statistics.
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