Transitions in non equilibrium systems

We study numerically the transition between organized and disorganized states of three non equilibrium systems in their respective scaling regimes. The first system is the Poisson/coalesce random walk (PCRW) where the particles describe independent random walks and when two particles meet they could coalesce with probability k, otherwise, they interchange their positions. The second system is a quasi one dimensional gas, where the particles interact only by volume exclusion in presence of an external field. The last system is a one dimensional spin lattice, where the particles interact by a coupling force J in presence of an external field. From our simulations we calculate the average spacing between particles/domain borders 〈s(t)〉. We found that 〈s(t)〉 has a similar behavior in the PCRW and gas cases but it is different in the spin system. Additionally, we use the Berry-Robnik model, the Abul-Magd model and the independent interval approximation to find an analytical approximation to the spacing distribution functions p(n)(s) and the pair correlation function g(r) for these systems. In all cases the nearest neighbor distribution is well described by these models. Unfortunately this does not happen with higher spacing distribution functions and the pair correlation functions. The analytical models proposed allow us to quantify the degree of order/disorder of the system by means of a parameter q. This parameter sets the system in an organized or disorganized state. [email protected] [email protected] 1