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Title: Asymptotic behaviour of time averages for non-ergodic Gaussian processes

Abstract

In this work, we study the behaviour of time-averages for stationary (non-ageing), but ergodicity-breaking Gaussian processes using their representation in Fourier space. We provide explicit formulae for various time-averaged quantities, such as mean square displacement, density, and analyse the behaviour of time-averaged characteristic function, which gives insight into rich memory structure of the studied processes. Moreover, we show applications of the ergodic criteria in Fourier space, determining the ergodicity of the generalised Langevin equation’s solutions. - Highlights: Ergodic criteria for Gaussian models which use Fourier transform are provided. Smooth, field Hamiltonian models are ergodic, discrete models are non-ergodic. Fractal Fourier structure can induce recurring correlations and non-mixing. Non-ergodic models exhibit non-linear dynamics and complex constants of motion. This non-linearity can be studied using time-averaged characteristic function.

Authors:
Publication Date:
OSTI Identifier:
22701516
Resource Type:
Journal Article
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 383; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; FOURIER TRANSFORMATION; GAUSSIAN PROCESSES; LANGEVIN EQUATION; NONLINEAR PROBLEMS

Citation Formats

Ślęzak, Jakub. Asymptotic behaviour of time averages for non-ergodic Gaussian processes. United States: N. p., 2017. Web. doi:10.1016/J.AOP.2017.05.015.
Ślęzak, Jakub. Asymptotic behaviour of time averages for non-ergodic Gaussian processes. United States. doi:10.1016/J.AOP.2017.05.015.
Ślęzak, Jakub. Tue . "Asymptotic behaviour of time averages for non-ergodic Gaussian processes". United States. doi:10.1016/J.AOP.2017.05.015.
@article{osti_22701516,
title = {Asymptotic behaviour of time averages for non-ergodic Gaussian processes},
author = {Ślęzak, Jakub},
abstractNote = {In this work, we study the behaviour of time-averages for stationary (non-ageing), but ergodicity-breaking Gaussian processes using their representation in Fourier space. We provide explicit formulae for various time-averaged quantities, such as mean square displacement, density, and analyse the behaviour of time-averaged characteristic function, which gives insight into rich memory structure of the studied processes. Moreover, we show applications of the ergodic criteria in Fourier space, determining the ergodicity of the generalised Langevin equation’s solutions. - Highlights: Ergodic criteria for Gaussian models which use Fourier transform are provided. Smooth, field Hamiltonian models are ergodic, discrete models are non-ergodic. Fractal Fourier structure can induce recurring correlations and non-mixing. Non-ergodic models exhibit non-linear dynamics and complex constants of motion. This non-linearity can be studied using time-averaged characteristic function.},
doi = {10.1016/J.AOP.2017.05.015},
journal = {Annals of Physics},
issn = {0003-4916},
number = ,
volume = 383,
place = {United States},
year = {2017},
month = {8}
}