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

| Peer-Reviewed

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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), 2024. Published by Science Publishing Group

Keywords

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

References

[1]	M.Tchoffo and A.A.Beilinson, “path integral approach to the kinematical Brownian motion due to random canonical transformation.” Far East J.Appl.Math 36, 1, 2009, pp.25-36
[2]	S.Massou, M.Tchoffo, “Factorization of the solution of Fokker-planck equation,” Far East J.Appl.Math volume 10, 2, 2012, pp.161-170.
[3]	M.Tchoffo, J.C. Ngana et al “Kinematical Brownian motion and time dependent entropy”, Far east J. vol 68, 1, 2012, pp. 21-28.
[4]	Massou. S, Moussiliou. S and M.Tchoffo ,“stochastic chaos in a class of Fokker-equation derived from population dynamic”, Applied Physics research 4, 3, 2012.
[5]	LY.Chen, P.L.Nash, “Stochastic Simulations of Clusters: Quantum Methods in Flat and Curved Spaces”, journal of chemical physics 121, 9, 2004.
[6]	Yu L klimontovich, “Nonlinear Brownian motion physics-Uspekhi” 37, 8, 1994, pp.737-767.
[7]	J.L.F. Barbón, “Pertubing The groundring of 2D String theory”, Int.J. Mod.Phys. A 07, 7579, 1992.
[8]	Achim Kempf, “Quantum integration on non-commutative geometries”, polish academy of science 40, 1997.
[9]	S. Paul Smith, “integral non-commutative space”, journal of algebra 246, 2001, pp.793-810.
[10]	Hugo Garcia, octa-vio Obregon et al, “Non-commutativity in gravity, topological gravity and cosmology” J of phys (conference serie) 24, 2005, pp.203-212.
[11]	J.C Ferrando, L.M.Sanchez, R. R. Mountain: “A survey on recent advances on the nikodim boundeness theorem and space of simple function” J.math 34, 2004, pp.139-172.
[12]	S. A. A Ghorashi, M.Bagheri Harouni, “Decoherence of quantum Brownian motion in non commutative space” physic letters A 377, 2013, pp.952-956.
[13]	V.P.Belavkin, “quantum ito B-algebras, their classification and decomposi-tion”, polish academy of science 43, 1998 .
[14]	wlod ziemerz bryz and victor bryc, “strong mixing coefficient for non-commutative Gaussian process”, proc Amer.math. soc 132, 2004, pp.523-534.
[15]	R.Vilela Mendes, “Quantum mechanics and non-commutative space”, physics letters A 210, 1996, pp.232-240.
[16]	A. Jahan, “non commutative harmonic oscillator at finite temperature”, a path integral approach, Brazilian journal of physics, 37, 2007.
[17]	Branko Dragovich, Zoran Rakic, “path integral in non-commutative quantum mechanics”, Theoretical and math phys 140, 3, 2004. pp.1299-1308.
[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.
[20]	Jean Zinn-Justin, "intégrale de chemin en mécanique quantique ", (EDP Sciences/CNRS editions, 2003).
[21]	A.E. Bernadini and O.Bertolami, “Probing phase-space non-commutativity through quantum beating, missing information and the thermodynamic limit”, Phys.Rev A 88, 012101, 2013.
[22]	Adil Belhaj, M.chabab et al, “on non-commutative Black holes and their thermodynamics in arbitrary dimension”, The African review of physics 8, 0017, 2013.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

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; Department of Physics, University of Buea, Buea, 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; Department of Thermal Engineering and Energetic, Douala University Institute of Technology, Douala, Cameroon
Lukong Cornelius Fai

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

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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