Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes

Abstract

We investigate the stochastic behavior of the single-trajectory spectral density $S(\omega ,\mathcal{T})$ of several Gaussian stochastic processes, i.e., Brownian motion, the Ornstein-Uhlenbeck process, the Brownian gyrator model and fractional Brownian motion, as a function of the frequency $\omega$ and the observation time $\mathcal{T}$. We evaluate in particular the variance and the frequency-frequency correlation of $S(\omega ,\mathcal{T})$ for different values of $\omega$. We show that these properties exhibit different behaviors for different physical cases and can therefore be used as a sensitive probe discriminating between different kinds of random motion. These results may prove quite useful in the analysis of experimental data.

29 pages, 7 figures

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Cited by in corpus (1)

• Fractional Brownian Gyrator