Correlation function in stochastic periodically driven instabilities

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Abstract
An alternative theoretical treatment of the order-disorder transition in periodically driven instabilities such as Rayleigh-Bénard convection is presented. The decay of the correlation function of the order parameter is calculated by using a general eigenvalue analysis of the Kolmogorov operator. It is shown that the boundary between stochastic and deterministic behavior found experimentally can be understood as a transition between regimes where the order parameter is, respectively, statistically uncorrelated and correlated in subsequent time periods.