Related Experiment Video
Updated: Jul 19, 2026

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
Published on: August 22, 2017
Spectral correlations of fractional Brownian motion
Tor Arne Øigård1, Alfred Hanssen, Louis L Scharf
1Department of Physics and Technology, University of Tromsø, NO-9037 Tromsø, Norway.
Abstract:
Fractional Brownian motion (fBm) is a ubiquitous nonstationary model for many physical processes with power-law time-averaged spectra. In this paper, we exploit the nonstationarity to derive the full spectral correlation structure of fBm. Starting from the time-varying correlation function, we derive two different time-frequency spectral correlation functions (the ambiguity function and the Kirkwood-Rihaczek spectrum), and one dual-frequency spectral correlation function. The dual-frequency spectral correlation has a surprisingly simple structure, with spectral support on three discrete lines. The theoretical predictions are verified by spectrum estimates of Monte Carlo simulations and of a time series of earthquakes with a magnitude of 7 and higher.
More Related Videos
Related Concept Videos
IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration
According to Hooke's law, the vibrational frequency is directly proportional to the...
¹H NMR: Interpreting Distorted and Overlapping Signals
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations
IR Spectroscopy: Molecular Vibration Overview
Stretching vibrations are vibrational motions that occur along the bond line, changing the bond length or distance between two bonded atoms. They are further distinguished as symmetric or asymmetric. In symmetric stretching, the...
Distribution of Molecular Speeds
Fermi Level Dynamics
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...

