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.
2022
Gaussian stochastic process; power spectral density; frequency-frequency correlation function
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1680168
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