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Transitions in non equilibrium systems

By Diego Luis González and Gabriel Téllez

Abstract

We study numerically the transition between organized and disorganized states of three non equilibrium systems. 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 driving 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. In order to find an analytical approximation to the normalized spacing distribution functions p (n) (s) and the pair correlation function g(r) for these systems, we propose a simple model where there are two kind of particles. This model can be solved analytically and it is statistically equivalent to the Berry-Robnik model. The Berry-Robnik model is used to study transitions in quantum systems and allows 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. The statistical behavior of the PCRW is well described by the Berry-Robnik model. For the gas and spi

Topics: Systems out of equilibrium, random matrices and Berry- Robnik model
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