We investigate the stochastic behavior of the single-trajectory spectral density S(omega,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 w and the observation time T. We evaluate in particular the variance and the frequency-frequency correlation of S(omega,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 and numerical data.
Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes / Squarcini, Alessio; Marinari, Vincenzo; Oshanin, Gleb; Peliti, Luca; Rondoni, Lamberto. - In: NEW JOURNAL OF PHYSICS. - ISSN 1367-2630. - 24:9(2022), p. 093031. [10.1088/1367-2630/ac8f65]
Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes
Enzo Marinari;Lamberto Rondoni
2022
Abstract
We investigate the stochastic behavior of the single-trajectory spectral density S(omega,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 w and the observation time T. We evaluate in particular the variance and the frequency-frequency correlation of S(omega,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 and numerical data.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.