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Fermiyon Benzeri İnstanton Çözümlerinin Dalgacık Entropi Analizinin İncelenmesi

Year 2022, , 972 - 978, 27.10.2022
https://doi.org/10.35414/akufemubid.1122381

Abstract

İnstantonlar klasik topolojik çözümlerdir, parçacık fiziği ve kozmolojide önemli rol oynarlar. Bu çalışmada, Heisenberg anzatıyla elde edilen iki boyutlu Thirring modelde fermiyon benzeri instanton çözümlerinin yörüngelerinin periyodikliği incelenmiştir. Fermiyon benzeri instanton çözümlerinin yörüngeleri, Shannon dalgacık entropisi (WE) yöntemi kullanılarak incelenmektedir. Ayrıca, faz uzayında WE ve WE spektrumları, fermiyon benzeri instanton çözümlerinin yörüngelerinin karakteristiği hakkında bilgi sahibi olabilmek için analiz edilmektedir. Çalışma sonucunda, fermiyon benzeri instanton çözümlerinin kararlı nokta etrafında düzenli, diğer noktalarda ise düzensiz yörüngelere sahip olduğu görülmüştür. Ayrıca bilinen diğer entropi yöntemleriyle (Renyi entropi ve Tsallis entropi) karşılaştırılmış ve benzer sonuçlar gözlemlenmiştir.

Thanks

Bu makaleyi hazırlarken verdiği destek için K. Gediz Akdeniz'e teşekkür ederim.

References

  • Anderson, D.R., 2008, Information Theory and Entropy, Springer, New York, 61-95.
  • Ak, M., 2022. 4 Boyutlu Fermiyonik Modelde Kaosun Genelleştirilmiş Hizalama İndeksi Yöntemiyle İncelenmesi. Journal of the Institute of Science and Technology, 12 (2), 726-734.
  • Akdeniz, K.G., Smailagic, A., 1979. Classical solutions for fermionic models. II Nuovo Cimento A, 51, 345– 357.
  • Blanco, S., Figliola, A., Quian-Quiroga, R., Rosso, O.A., Serrano, E., 1998. Time–frequency analysis of electroencephalogram series (III): wavelet packets and information cost function. Physical Review E, 57, 932-940.
  • Boltzmann, L., 1871. Einige allgemeine Satze über Warmegleichgewicht unter Gas-molekulen, Sitzungsber. Akad Wiss Wien, 63, 679–711.
  • Bouzebda, S., Elhattab, I., 2014. New Kernel-types Estimator of Shannon’s Entropy. Comptes Rendus Mathematique, 352(1), 75–80.
  • Brown, R., 2018, A Modern Introduction to Dynamical Systems, Oxford University Press, 1-12.
  • Burrus, C.S., Gopinath, R.A., Guo, H., 1998, Introduction to Wavelets and Wavelet Transforms: A Primer. Prentice Hall, New Jersey, 15-37.
  • Canbaz, B., Onem, C., Aydogmus, F., Akdeniz, K.G., 2012. From Heisenberg ansatz to attractor of Thirring Instanton. Chaos, Solitons & Fractals, 45(2), 188–191.
  • Canbaz, B., 2022. Genel Hizalama İndeksi Yöntemiyle 2 Boyutlu Saf Fermiyonik Modelde Kaosun İncelenmesi. Avrupa Bilim ve Teknoloji Dergisi, 33, 161-166.
  • Canbaz B., 2022. Lyapunov Exponents of Thirring Instantons, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 11(2), 529-536.
  • Clausius, R., 1850. On the motive power of heat & on the laws which may be deduced from it for the theory of heat. Annalen der Physik, 79, 368-500.
  • Goswami, J.C., Chan, A.K., 1999, Fundamentals of Wavelets: Theory, Algorithms, and Applications, 2nd Edition, John Wiley & Sons, USA.
  • Heisenberg, W., 1954. Zur quantentheorie nichtrenormierbarer wellengleichungen. Zeitschrift für Naturforschung A, 9, 292–303.
  • Meyer, Y., 1993. Wavelets: Algorithms and Applications, SIAM, Philadelphia, 1-11.
  • Nicolis, O., Mateu, J., Contreras-Reyes, J.E., 2020. Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields. Entropy, 22(2), 196.
  • Renyi, A., 1970, Probability theory, Amsterdam: North-Holland.
  • Rosso, O.A., Mairal, M.L., 2002. Characterization of time dynamical evolution of electroencephalographic records. Physica A, 312, 469–504.
  • Shannon, C., 1948. A mathematical theory of communication. Bell System Technical Journal, 27, 379–423.
  • Shifman, M., 1994, Instantons In Gauge Theories, World Scientific Publishing Company.
  • Thirring, W., 1958. A Soluble Relativistic Field Theory. Annals of Physics, 3(1), 91-112.
  • Tsallis, C., 1988. Possible generalization of Boltzmann–Gibbs statistics. Journal of Statistical Physics, 52, 479–487.
  • Ubriaco, M.R., 2009. Entropies based on fractional calculus. Physics Letters A, 373(30), 2516–2519.
  • Yılmaz, N., Canbaz, B., Akıllı, M., Onem, C., 2018. Study of the stability of the fermionic instanton solutions by the scale index method. Physics Letters A, 382, 2118-2121.

Study of Wavelet Entropy Analysis of the Fermion-like Instanton Solutions

Year 2022, , 972 - 978, 27.10.2022
https://doi.org/10.35414/akufemubid.1122381

Abstract

Instantons are classical topological solutions, playing an important role in particle physics and cosmology. In this study, the periodicity of the orbits of the fermion-like instanton solutions in the two-dimensional Thirring model obtained with the Heisenberg ansatz is investigated. The trajectories of fermion-like instanton solutions are investigated by the Shannon wavelet entropy (WE) method. In addition, WE and WE spectrum in phase space are analyzed in order to have information about the characteristics of the trajectories of fermion-like instanton solutions. As a result of the study, it was seen that the fermion-like instanton solutions have regular trajectories around the stable point and irregular trajectories at other points. It was also compared with other known entropy methods (Renyi entropy and Tsallis entropy) and similar results were observed.

References

  • Anderson, D.R., 2008, Information Theory and Entropy, Springer, New York, 61-95.
  • Ak, M., 2022. 4 Boyutlu Fermiyonik Modelde Kaosun Genelleştirilmiş Hizalama İndeksi Yöntemiyle İncelenmesi. Journal of the Institute of Science and Technology, 12 (2), 726-734.
  • Akdeniz, K.G., Smailagic, A., 1979. Classical solutions for fermionic models. II Nuovo Cimento A, 51, 345– 357.
  • Blanco, S., Figliola, A., Quian-Quiroga, R., Rosso, O.A., Serrano, E., 1998. Time–frequency analysis of electroencephalogram series (III): wavelet packets and information cost function. Physical Review E, 57, 932-940.
  • Boltzmann, L., 1871. Einige allgemeine Satze über Warmegleichgewicht unter Gas-molekulen, Sitzungsber. Akad Wiss Wien, 63, 679–711.
  • Bouzebda, S., Elhattab, I., 2014. New Kernel-types Estimator of Shannon’s Entropy. Comptes Rendus Mathematique, 352(1), 75–80.
  • Brown, R., 2018, A Modern Introduction to Dynamical Systems, Oxford University Press, 1-12.
  • Burrus, C.S., Gopinath, R.A., Guo, H., 1998, Introduction to Wavelets and Wavelet Transforms: A Primer. Prentice Hall, New Jersey, 15-37.
  • Canbaz, B., Onem, C., Aydogmus, F., Akdeniz, K.G., 2012. From Heisenberg ansatz to attractor of Thirring Instanton. Chaos, Solitons & Fractals, 45(2), 188–191.
  • Canbaz, B., 2022. Genel Hizalama İndeksi Yöntemiyle 2 Boyutlu Saf Fermiyonik Modelde Kaosun İncelenmesi. Avrupa Bilim ve Teknoloji Dergisi, 33, 161-166.
  • Canbaz B., 2022. Lyapunov Exponents of Thirring Instantons, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 11(2), 529-536.
  • Clausius, R., 1850. On the motive power of heat & on the laws which may be deduced from it for the theory of heat. Annalen der Physik, 79, 368-500.
  • Goswami, J.C., Chan, A.K., 1999, Fundamentals of Wavelets: Theory, Algorithms, and Applications, 2nd Edition, John Wiley & Sons, USA.
  • Heisenberg, W., 1954. Zur quantentheorie nichtrenormierbarer wellengleichungen. Zeitschrift für Naturforschung A, 9, 292–303.
  • Meyer, Y., 1993. Wavelets: Algorithms and Applications, SIAM, Philadelphia, 1-11.
  • Nicolis, O., Mateu, J., Contreras-Reyes, J.E., 2020. Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields. Entropy, 22(2), 196.
  • Renyi, A., 1970, Probability theory, Amsterdam: North-Holland.
  • Rosso, O.A., Mairal, M.L., 2002. Characterization of time dynamical evolution of electroencephalographic records. Physica A, 312, 469–504.
  • Shannon, C., 1948. A mathematical theory of communication. Bell System Technical Journal, 27, 379–423.
  • Shifman, M., 1994, Instantons In Gauge Theories, World Scientific Publishing Company.
  • Thirring, W., 1958. A Soluble Relativistic Field Theory. Annals of Physics, 3(1), 91-112.
  • Tsallis, C., 1988. Possible generalization of Boltzmann–Gibbs statistics. Journal of Statistical Physics, 52, 479–487.
  • Ubriaco, M.R., 2009. Entropies based on fractional calculus. Physics Letters A, 373(30), 2516–2519.
  • Yılmaz, N., Canbaz, B., Akıllı, M., Onem, C., 2018. Study of the stability of the fermionic instanton solutions by the scale index method. Physics Letters A, 382, 2118-2121.
There are 24 citations in total.

Details

Primary Language Turkish
Subjects Metrology, Applied and Industrial Physics
Journal Section Articles
Authors

Beyrul Canbaz 0000-0002-5633-2296

Publication Date October 27, 2022
Submission Date May 27, 2022
Published in Issue Year 2022

Cite

APA Canbaz, B. (2022). Fermiyon Benzeri İnstanton Çözümlerinin Dalgacık Entropi Analizinin İncelenmesi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 22(5), 972-978. https://doi.org/10.35414/akufemubid.1122381
AMA Canbaz B. Fermiyon Benzeri İnstanton Çözümlerinin Dalgacık Entropi Analizinin İncelenmesi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. October 2022;22(5):972-978. doi:10.35414/akufemubid.1122381
Chicago Canbaz, Beyrul. “Fermiyon Benzeri İnstanton Çözümlerinin Dalgacık Entropi Analizinin İncelenmesi”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22, no. 5 (October 2022): 972-78. https://doi.org/10.35414/akufemubid.1122381.
EndNote Canbaz B (October 1, 2022) Fermiyon Benzeri İnstanton Çözümlerinin Dalgacık Entropi Analizinin İncelenmesi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22 5 972–978.
IEEE B. Canbaz, “Fermiyon Benzeri İnstanton Çözümlerinin Dalgacık Entropi Analizinin İncelenmesi”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 22, no. 5, pp. 972–978, 2022, doi: 10.35414/akufemubid.1122381.
ISNAD Canbaz, Beyrul. “Fermiyon Benzeri İnstanton Çözümlerinin Dalgacık Entropi Analizinin İncelenmesi”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22/5 (October 2022), 972-978. https://doi.org/10.35414/akufemubid.1122381.
JAMA Canbaz B. Fermiyon Benzeri İnstanton Çözümlerinin Dalgacık Entropi Analizinin İncelenmesi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2022;22:972–978.
MLA Canbaz, Beyrul. “Fermiyon Benzeri İnstanton Çözümlerinin Dalgacık Entropi Analizinin İncelenmesi”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 22, no. 5, 2022, pp. 972-8, doi:10.35414/akufemubid.1122381.
Vancouver Canbaz B. Fermiyon Benzeri İnstanton Çözümlerinin Dalgacık Entropi Analizinin İncelenmesi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2022;22(5):972-8.


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