Dynamics of Non-Equilibrium Systems Near Critical region of Phase Transition

Abstract

We study some of the properties of non-equilibrium phase transitions of an interacting system that is in a state with large deviation from equilibrium. We consider a field theoretical model of scalar particles interacting with vector gauge fields with local U (1) gauge symmetry. We show that the evolution of this system towards an equilbrium state can be described using the principle of emergence of global gauge invariance. As a toy model we consider a scalar-vector model with local U (1) gauge invariance. Invoking the assumption of local U (1) gauge invariance breaking we evaluate time evolution of some of the observables of this system. To make our calculations explicit we calculate the time evolution of order parameter of this sytem and evaluate its scaling behaviour near transition region. In the mean-field approximation we show that, for the unperturbed case, that correspond to no external driving the order parameter has a universal algebriac decay m(t) ∼ t −1/2 . However for time-dependent diffusion coefficient, it is found that order parametr has a universal algabriac decay m(t) ∼ t −1/3 . The results are in total agreement with the recent findings using stochastic models of non-equilibrium system