"Quantum phase transitions" in classical nonequilibrium processes

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  • 30 August 1999
Abstract
Diffusion limited reaction of the Lotka-Volterra type is analyzed taking into account the discrete nature of the reactants. In the continuum approximation, the dynamics is dominated by an elliptic fixed-point over the whole parameter space of the system. Discretization effects break the parameter space into several phases where the system exhibits a distinct behavior: The fixed-point becomes either stable (node or focus) or unstable (node or focus). The results are verified by extensive numerical simulations. These simulations also suggest that, in the unstable phase, a new ground state is formed, where the dynamics flows into a limit cycle.

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