The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative

Hong Lu; Yan Lü

doi:doi:10.11648/j.ajpa.20221002.12

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The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative

Hong Lu, Yan Lü

Published in American Journal of Physics and Applications (Volume 10, Issue 2)

Received: 16 February 2022 Accepted: 7 March 2022 Published: 14 March 2022

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Abstract

The diffusion behavior of the system driven by the non-Gaussian noise and its time derivative are investigated in detail. The temperature dependence of the noise spectral profile is firstly analyzed using Monte Carlo simulations, which is shown that the spectrum of the non-Gaussian noise is a decreasing function of temperature when the frequency is sufficient small. By contrast, its derivative is Gaussian and vanishes for the low frequency. In addition, diffusion behavior of the system subjected to non Gaussian noise or its time derivative are more detailed discussed within the framework of the generalized Langevin equation. It is particularly revealed that the system driven by the internal non-Gaussian noise behaves as normal diffusion for various temperatures, while the time derivative of the non-Gaussian noise induces ballistic diffusion of a free system and the variance is sensitive to the initial condition which implies the breaking of the ergodicity.

Published in	American Journal of Physics and Applications (Volume 10, Issue 2)
DOI	10.11648/j.ajpa.20221002.12
Page(s)	33-37
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Non-Gaussian Noise, Ballistic Diffusion, Monte Carlo Simulations

References

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Hong Lu, Yan Lü. (2022). The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative. American Journal of Physics and Applications, 10(2), 33-37. https://doi.org/10.11648/j.ajpa.20221002.12

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ACS Style

Hong Lu; Yan Lü. The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative. Am. J. Phys. Appl. 2022, 10(2), 33-37. doi: 10.11648/j.ajpa.20221002.12

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AMA Style

Hong Lu, Yan Lü. The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative. Am J Phys Appl. 2022;10(2):33-37. doi: 10.11648/j.ajpa.20221002.12

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@article{10.11648/j.ajpa.20221002.12,
  author = {Hong Lu and Yan Lü},
  title = {The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative},
  journal = {American Journal of Physics and Applications},
  volume = {10},
  number = {2},
  pages = {33-37},
  doi = {10.11648/j.ajpa.20221002.12},
  url = {https://doi.org/10.11648/j.ajpa.20221002.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20221002.12},
  abstract = {The diffusion behavior of the system driven by the non-Gaussian noise and its time derivative are investigated in detail. The temperature dependence of the noise spectral profile is firstly analyzed using Monte Carlo simulations, which is shown that the spectrum of the non-Gaussian noise is a decreasing function of temperature when the frequency is sufficient small. By contrast, its derivative is Gaussian and vanishes for the low frequency. In addition, diffusion behavior of the system subjected to non Gaussian noise or its time derivative are more detailed discussed within the framework of the generalized Langevin equation. It is particularly revealed that the system driven by the internal non-Gaussian noise behaves as normal diffusion for various temperatures, while the time derivative of the non-Gaussian noise induces ballistic diffusion of a free system and the variance is sensitive to the initial condition which implies the breaking of the ergodicity.},
 year = {2022}
}

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TY  - JOUR
T1  - The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative
AU  - Hong Lu
AU  - Yan Lü
Y1  - 2022/03/14
PY  - 2022
N1  - https://doi.org/10.11648/j.ajpa.20221002.12
DO  - 10.11648/j.ajpa.20221002.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 33
EP  - 37
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20221002.12
AB  - The diffusion behavior of the system driven by the non-Gaussian noise and its time derivative are investigated in detail. The temperature dependence of the noise spectral profile is firstly analyzed using Monte Carlo simulations, which is shown that the spectrum of the non-Gaussian noise is a decreasing function of temperature when the frequency is sufficient small. By contrast, its derivative is Gaussian and vanishes for the low frequency. In addition, diffusion behavior of the system subjected to non Gaussian noise or its time derivative are more detailed discussed within the framework of the generalized Langevin equation. It is particularly revealed that the system driven by the internal non-Gaussian noise behaves as normal diffusion for various temperatures, while the time derivative of the non-Gaussian noise induces ballistic diffusion of a free system and the variance is sensitive to the initial condition which implies the breaking of the ergodicity.
VL  - 10
IS  - 2
ER  -

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Author Information

Hong Lu

School of Science, Guizhou University of Engineering Science, P. R. China
Yan Lü

School of Applied Science, Taiyuan University of Science and Technology, P. R. China

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APA Style

Hong Lu, Yan Lü. (2022). The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative. American Journal of Physics and Applications, 10(2), 33-37. https://doi.org/10.11648/j.ajpa.20221002.12

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ACS Style

Hong Lu; Yan Lü. The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative. Am. J. Phys. Appl. 2022, 10(2), 33-37. doi: 10.11648/j.ajpa.20221002.12

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AMA Style

Hong Lu, Yan Lü. The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative. Am J Phys Appl. 2022;10(2):33-37. doi: 10.11648/j.ajpa.20221002.12

Copy | Download

@article{10.11648/j.ajpa.20221002.12,
  author = {Hong Lu and Yan Lü},
  title = {The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative},
  journal = {American Journal of Physics and Applications},
  volume = {10},
  number = {2},
  pages = {33-37},
  doi = {10.11648/j.ajpa.20221002.12},
  url = {https://doi.org/10.11648/j.ajpa.20221002.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20221002.12},
  abstract = {The diffusion behavior of the system driven by the non-Gaussian noise and its time derivative are investigated in detail. The temperature dependence of the noise spectral profile is firstly analyzed using Monte Carlo simulations, which is shown that the spectrum of the non-Gaussian noise is a decreasing function of temperature when the frequency is sufficient small. By contrast, its derivative is Gaussian and vanishes for the low frequency. In addition, diffusion behavior of the system subjected to non Gaussian noise or its time derivative are more detailed discussed within the framework of the generalized Langevin equation. It is particularly revealed that the system driven by the internal non-Gaussian noise behaves as normal diffusion for various temperatures, while the time derivative of the non-Gaussian noise induces ballistic diffusion of a free system and the variance is sensitive to the initial condition which implies the breaking of the ergodicity.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - The Diffusion Behavior of the System Driven by Non-Gaussian Noise or Its Time Derivative
AU  - Hong Lu
AU  - Yan Lü
Y1  - 2022/03/14
PY  - 2022
N1  - https://doi.org/10.11648/j.ajpa.20221002.12
DO  - 10.11648/j.ajpa.20221002.12
T2  - American Journal of Physics and Applications
JF  - American Journal of Physics and Applications
JO  - American Journal of Physics and Applications
SP  - 33
EP  - 37
PB  - Science Publishing Group
SN  - 2330-4308
UR  - https://doi.org/10.11648/j.ajpa.20221002.12
AB  - The diffusion behavior of the system driven by the non-Gaussian noise and its time derivative are investigated in detail. The temperature dependence of the noise spectral profile is firstly analyzed using Monte Carlo simulations, which is shown that the spectrum of the non-Gaussian noise is a decreasing function of temperature when the frequency is sufficient small. By contrast, its derivative is Gaussian and vanishes for the low frequency. In addition, diffusion behavior of the system subjected to non Gaussian noise or its time derivative are more detailed discussed within the framework of the generalized Langevin equation. It is particularly revealed that the system driven by the internal non-Gaussian noise behaves as normal diffusion for various temperatures, while the time derivative of the non-Gaussian noise induces ballistic diffusion of a free system and the variance is sensitive to the initial condition which implies the breaking of the ergodicity.
VL  - 10
IS  - 2
ER  -

Copy | Download