Interacting Stochastic Particle Systems

According to the basic principles of mechanics, the motion of atoms and molecules is governed, in the semiclassical approximation, by the deterministic Hamiltonian equations of motion. While all evidence points in this direction, for many problems this Hamiltonian approach is so complicated that it hardly yields any useful results. A simple example are many (10⁹) polystyrene balls (size 1 nm) immersed in water. The Hamiltonian description would have to deal with the degrees of freedom of all the fluid molecules and all the polystyrene balls. Clearly, a more useful approach is to collect the incessant bombardment of a polystyrene ball by water molecules into a stochastic force acting on the ball with postulated statistical properties. For example, following Einstein, one could regard successive collisions as independent and occurring after an exponentially distributed waiting time. In addition to such stochastic forces, the polystyrene balls are charged and interact with each other through the screened Coulomb force.