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

Abstract We investigate the stochastic behavior of the single-trajectory spectral density S ( ω , 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 ω and the o...

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Bibliographic Details
Published in:	New journal of physics Vol. 24; no. 9
Main Authors:	Squarcini, Alessio, Marinari, Enzo, Oshanin, Gleb, Peliti, Luca, Rondoni, Lamberto
Format:	Journal Article
Language:	English
Published:	Institute of Physics: Open Access Journals 27-09-2022
Subjects:	Mathematics Physics spectral densities, frequency-frequency correlations, spectral noise
Online Access:	Get full text
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Summary:	Abstract We investigate the stochastic behavior of the single-trajectory spectral density S ( ω , 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 ω and the observation time T . We evaluate in particular the variance and the frequency–frequency correlation of S ( ω , T ) for different values of ω . 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.
ISSN:	1367-2630 1367-2630
DOI:	10.1088/1367-2630/ac8f65