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

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 observatio...

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Bibliographic Details
Published in:New journal of physics 2022-09, Vol.24 (9), p.93031
Main Authors: Squarcini, Alessio, Marinari, Enzo, Oshanin, Gleb, Peliti, Luca, Rondoni, Lamberto
Format: Article
Language:English
Subjects:
Behavior
Brownian motion
frequency–frequency correlation function
Gaussian process
Gaussian stochastic process
Mathematics
Physics
power spectral density
Quantum dots
Random variables
Stochastic models
Stochastic processes
Time series
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Summary: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