Stochastic model related to the Klein-Gordon equation.

In this note, a one-dimensional system composed of an assembly of interacting particles, is considered. Each particle in the assembly moves in a well-defined trajectory on a line with a velocity of fixed magnitude, which randomly reverses direction. The intrinsic forces in the system are assumed to induce stochastic transitions between velocity states in such a way that the average dynamics of the assembly is Newtonian. It is shown that there is a close analogy between collective oscillations in the model system and the propagation of a free quantum particle in one dimension.