Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space

Martin Tchoffo; Jules Casimir Ngana Kuetche; Georges Collince Fouokeng; Ngwa Engelbert Afuoti; Lukong Cornelius Fai

doi:doi:10.11648/j.ajmp.20140303.14

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Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space

Martin Tchoffo, Jules Casimir Ngana Kuetche, Georges Collince Fouokeng, Ngwa Engelbert Afuoti, Lukong Cornelius Fai

Published in American Journal of Modern Physics (Volume 3, Issue 3)

Received: 2 May 2014 Accepted: 20 May 2014 Published: 30 May 2014

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Abstract

In this work the Jacobi’s second equality in the form of stochastic equation and the Wiener path integral approach are used to evaluate the probability density of harmonic oscillator in non-commutative space. Using the factorization theorem and the Mastubara formalism, the thermodynamic parameters are determined. The structure of Fokker-Planck equation remained the same even in a commutative and non-commutative space. Moreover, the non-commutative parameter is depicted for increasing value of the entropy.

Published in	American Journal of Modern Physics (Volume 3, Issue 3)
DOI	10.11648/j.ajmp.20140303.14
Page(s)	138-142
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), 2014. Published by Science Publishing Group

Keywords

Brownian Motion, Stochastic Equation, Wiener Process, Fokker-Planck Equation, Non-Commutative Space

References

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APA Style

Martin Tchoffo, Jules Casimir Ngana Kuetche, Georges Collince Fouokeng, Ngwa Engelbert Afuoti, Lukong Cornelius Fai. (2014). Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space. American Journal of Modern Physics, 3(3), 138-142. https://doi.org/10.11648/j.ajmp.20140303.14

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ACS Style

Martin Tchoffo; Jules Casimir Ngana Kuetche; Georges Collince Fouokeng; Ngwa Engelbert Afuoti; Lukong Cornelius Fai. Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space. Am. J. Mod. Phys. 2014, 3(3), 138-142. doi: 10.11648/j.ajmp.20140303.14

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AMA Style

Martin Tchoffo, Jules Casimir Ngana Kuetche, Georges Collince Fouokeng, Ngwa Engelbert Afuoti, Lukong Cornelius Fai. Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space. Am J Mod Phys. 2014;3(3):138-142. doi: 10.11648/j.ajmp.20140303.14

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@article{10.11648/j.ajmp.20140303.14,
  author = {Martin Tchoffo and Jules Casimir Ngana Kuetche and Georges Collince Fouokeng and Ngwa Engelbert Afuoti and Lukong Cornelius Fai},
  title = {Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space},
  journal = {American Journal of Modern Physics},
  volume = {3},
  number = {3},
  pages = {138-142},
  doi = {10.11648/j.ajmp.20140303.14},
  url = {https://doi.org/10.11648/j.ajmp.20140303.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20140303.14},
  abstract = {In this work the Jacobi’s second equality in the form of stochastic equation and the Wiener path integral approach are used to evaluate the probability density of harmonic oscillator in non-commutative space. Using the factorization theorem and the Mastubara formalism, the thermodynamic parameters are determined. The structure of Fokker-Planck equation remained the same even in a commutative and non-commutative space. Moreover, the non-commutative parameter is depicted for increasing value of the entropy.},
 year = {2014}
}

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TY  - JOUR
T1  - Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space
AU  - Martin Tchoffo
AU  - Jules Casimir Ngana Kuetche
AU  - Georges Collince Fouokeng
AU  - Ngwa Engelbert Afuoti
AU  - Lukong Cornelius Fai
Y1  - 2014/05/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajmp.20140303.14
DO  - 10.11648/j.ajmp.20140303.14
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 138
EP  - 142
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20140303.14
AB  - In this work the Jacobi’s second equality in the form of stochastic equation and the Wiener path integral approach are used to evaluate the probability density of harmonic oscillator in non-commutative space. Using the factorization theorem and the Mastubara formalism, the thermodynamic parameters are determined. The structure of Fokker-Planck equation remained the same even in a commutative and non-commutative space. Moreover, the non-commutative parameter is depicted for increasing value of the entropy.
VL  - 3
IS  - 3
ER  -

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Author Information

Martin Tchoffo

Mesoscopic and Multilayer Structures Laboratory, Department of Physics, University of Dschang, Cameroon
Jules Casimir Ngana Kuetche

Mesoscopic and Multilayer Structures Laboratory, Department of Physics, University of Dschang, Cameroon
Georges Collince Fouokeng

Mesoscopic and Multilayer Structures Laboratory, Department of Physics, University of Dschang, Cameroon
Ngwa Engelbert Afuoti

Mesoscopic and Multilayer Structures Laboratory, Department of Physics, University of Dschang, Cameroon
Lukong Cornelius Fai

Mesoscopic and Multilayer Structures Laboratory, Department of Physics, University of Dschang, Cameroon

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APA Style

Martin Tchoffo, Jules Casimir Ngana Kuetche, Georges Collince Fouokeng, Ngwa Engelbert Afuoti, Lukong Cornelius Fai. (2014). Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space. American Journal of Modern Physics, 3(3), 138-142. https://doi.org/10.11648/j.ajmp.20140303.14

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ACS Style

Martin Tchoffo; Jules Casimir Ngana Kuetche; Georges Collince Fouokeng; Ngwa Engelbert Afuoti; Lukong Cornelius Fai. Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space. Am. J. Mod. Phys. 2014, 3(3), 138-142. doi: 10.11648/j.ajmp.20140303.14

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AMA Style

Martin Tchoffo, Jules Casimir Ngana Kuetche, Georges Collince Fouokeng, Ngwa Engelbert Afuoti, Lukong Cornelius Fai. Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space. Am J Mod Phys. 2014;3(3):138-142. doi: 10.11648/j.ajmp.20140303.14

Copy | Download

@article{10.11648/j.ajmp.20140303.14,
  author = {Martin Tchoffo and Jules Casimir Ngana Kuetche and Georges Collince Fouokeng and Ngwa Engelbert Afuoti and Lukong Cornelius Fai},
  title = {Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space},
  journal = {American Journal of Modern Physics},
  volume = {3},
  number = {3},
  pages = {138-142},
  doi = {10.11648/j.ajmp.20140303.14},
  url = {https://doi.org/10.11648/j.ajmp.20140303.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20140303.14},
  abstract = {In this work the Jacobi’s second equality in the form of stochastic equation and the Wiener path integral approach are used to evaluate the probability density of harmonic oscillator in non-commutative space. Using the factorization theorem and the Mastubara formalism, the thermodynamic parameters are determined. The structure of Fokker-Planck equation remained the same even in a commutative and non-commutative space. Moreover, the non-commutative parameter is depicted for increasing value of the entropy.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space
AU  - Martin Tchoffo
AU  - Jules Casimir Ngana Kuetche
AU  - Georges Collince Fouokeng
AU  - Ngwa Engelbert Afuoti
AU  - Lukong Cornelius Fai
Y1  - 2014/05/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajmp.20140303.14
DO  - 10.11648/j.ajmp.20140303.14
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 138
EP  - 142
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20140303.14
AB  - In this work the Jacobi’s second equality in the form of stochastic equation and the Wiener path integral approach are used to evaluate the probability density of harmonic oscillator in non-commutative space. Using the factorization theorem and the Mastubara formalism, the thermodynamic parameters are determined. The structure of Fokker-Planck equation remained the same even in a commutative and non-commutative space. Moreover, the non-commutative parameter is depicted for increasing value of the entropy.
VL  - 3
IS  - 3
ER  -

Copy | Download