"Quantum phase transitions" in classical nonequilibrium processes

TL;DR

This paper investigates how discretization effects in classical nonequilibrium processes lead to phase transition-like behavior, causing a shift from fixed-point dynamics to limit cycles, verified through numerical simulations.

Contribution

It introduces the concept of quantum phase transition analogs in classical systems due to discretization effects, a novel perspective in nonequilibrium process analysis.

Findings

Discretization destabilizes the elliptic fixed-point.

System dynamics shift to a limit cycle due to discretization.

Numerical simulations confirm the theoretical predictions.

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. This fixed-point becomes unstable due to discretization effects, a scenario similar to quantum phase transitions. As a result, the long-time asymptotic behavior of the system changes and the dynamics flows into a limit cycle. The results are verified by numerical simulations.