A binary-quantized pseudo-diffusion system

A binary-quantized cellular array model of linear diffusion systems is investigated microscopically by introducing virtual particles. A deterministic rule applied to all the cells of the array determines the motion of the particles in the array. The probabilistic distribution in terms of the displacement of the particles in the array is similar to a Gaussian distribution, and its variance increases in proportion to time. The discontinuous velocity of the particles has almost uniform frequency spectrum distribution and delta-function-like autocorrelation. Thus, the virtual particles whose behavior is deterministic possess almost the same characteristics that probabilistic Brownian particles in diffusion systems have. We conclude that the cellular array is an excellent binary-quantized and discrete pseudo-diffusion system.