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

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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[16] A. Jahan, “non commutative harmonic oscillator at finite temperature”, a path integral approach, Brazilian journal of physics, 37, 2007.
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[18] M.Chaichian, A.Tureanu, A.Zahahi “solution of the stochastic Langevin equations for clustering of particles in random flows in terms of the wiener path integral”, Phys.Rev. E 81, 066309, 2010 .
[19] Iraj Jabbari, Akbar Jahan, and Zafar Riaziturk “Partition function of the harmonic oscillator on a non commutative plane”, J.phys 33, 2009, pp.149-154.
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Cite This Article
  • 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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    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
  • Mesoscopic and Multilayer Structures Laboratory, Department of Physics, University of Dschang, Cameroon

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

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

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

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

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