Golden ratio autocorrelation function and the exponential decay

An autocorrelation function is obtained on the base of the recurrence relation formalism, whose continued fraction form corresponds to that of golden ratio. It turns out that this GR autocorrelation is known in science and obeys all necessary conditions, in contrast to the exponential autocorrelation function. Using the Kubo approach it is shown how exponential correlations appear in the linear response theory as a result of non-Hermitian relaxation of the system.