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4 Boyutlu Fermiyonik Modelde Kaosun Genelleştirilmiş Hizalama İndeksi Yöntemiyle İncelenmesi

Year 2022, Volume: 12 Issue: 2, 726 - 734, 01.06.2022
https://doi.org/10.21597/jist.1047562

Abstract

İnstantonlar, soliton tipi çözümler olup, konformal simetrinin kırılması sonucu elde edilmişlerdir. Uzay zaman açılımına sahip olup, kuantum karakteri taşımalarından dolayı kuarkların vakum durumu olarak tanımlanırlar. Heisenberg’in sunduğu sadece fermiyonlardan oluşan modele alternatif olarak sunulan modellerden biri de 4 boyutlu konformal invaryant saf fermiyonik Gürsey Modeldir. Bu çalışmanın amacı, Gürsey instantonlarının çözümlerinin kaotikliğini ve sistemin dinamiğini Genelleştirilmiş Hizalama İndeksi (GALI) yönteminden yararlanarak incelemektir. Yörüngelerdeki kaosu ve düzenli hareketi hızlı ve güvenli bir şekilde tespit edebilmesi, yarı periyodik hareketin meydana geldiği torusun boyutsallığını belirleyebilmesi Genelleştirilmiş Hizalama İndeksi (GALI) yöntemini önemli kılmaktadır. Bu çalışmada, Gürsey instanton çözümlerinin kaotikliği Genelleştirilmiş Hizalama İndeksi (GALI) yöntemiyle araştırılmıştır.

Thanks

Bu makaleyi hazırlarken verdiği destek için değerli hocam Prof. Dr. K.Gediz AKDENİZ’e teşekkür ederim.

References

  • Akdeniz KG, 1982. On classical solutions of Gursey’s conformal-invariant spinor model. Lettere al Nuovo Cimento, 33(2): 40–44.
  • Antonopoulos C, Bountis T, 2006. Detecting order and chaos by the linear dependence index method. Romai Journal, 2(2): 1-13.
  • Aydogmus F, Canbaz B, Onem C, Akdeniz KG, 2013. The behaviours of Gursey instantons in phase space. Acta Physica Polonica B, 44(9): 1837–1845.
  • Belitsky AV, Vandoren S, Van Nieuwenhuizen P, 2000. Yang-Mills and D-instantons. Classical and Quantum Gravity, 17(17): 3521-3570.
  • Christodoulidi H, Bountis T, 2006. Low-dimensional quasiperiodic motion in hamiltonian systems. Romai Journal 2(2): 37-44.
  • Gursey F, 1956. On a conform-invariant spinor wave equation. Il Nuovo Cimento, 3(5): 988–1006.
  • Heisenberg W, 1954. Zur quantentheorie nichtrenormierbarer wellengleichungen. Zeitschrift für Naturforschung A, 9, 292–303.
  • Kortel F, 1956. On some solutions of Gursey’s conformal-invariant spinor wave equation. Il Nuovo Cimento, 4, 210–215.
  • Manos T, Skokos C, Antonopoulos C, 2012. Probing the local dynamics of periodic orbits by the Generalized Alignment Index (GALI) method. International Journal of Bifurcation and Chaos, 22(9): 1250218.
  • Moges HT, 2020. Investigating Chaos by the Generalized Alignment Index (GALI) Method. University of Cape Town.
  • Olive D, Sciuto S, Crewther RJ, 1979. Instantons in field theory. La Rivista del Nuovo Cimento, 2(8): 1-117.
  • Paranjape M, 2018. The theory and applications of instanton calculations. Cambridge University Press, England.
  • Senyange B, Skokos C, 2022. Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method. Physica D: Nonlinear Phenomena, 432: 133154.
  • Shifman M, 1994. Instantons in gauge theories. World Scientific, Singapore.
  • Skokos C, Bountis T, Antonopoulos C, 2007. Geometrical properties of local dynamics in hamiltonian systems: the Generalized Alignment Index (GALI) method. Physica D, 231(1): 30-54.
  • Skokos C, Bountis T, Antonopoulos C, 2008. Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi-Pasta-Ulam lattices by the Generalized Alignment Index method. The European Physical Journal Special Topics, 165(1): 5-14.

Investigation of Chaos in 4D Fermionic Model by the Generalized Alignment Index Method

Year 2022, Volume: 12 Issue: 2, 726 - 734, 01.06.2022
https://doi.org/10.21597/jist.1047562

Abstract

Instantons are soliton-type solutions and are obtained as a result of breaking the conformal symmetry. They have space-time expansion and are defined as the vacuum state of quarks due to their quantum character. One of the models offered as an alternative to the model consisting of only fermions offered by Heisenberg is the 4-dimensional conformal invariant pure fermionic Gursey Model. The aim of this study is to examine the chaoticity of the solutions of Gursey instantons and the dynamics of the system by using the Generalized Alignment Index (GALI) method. The fact that it can detect the chaos and regular motion in the orbits quickly and safely and determine the dimensionality of the torus in which the quasi-periodic motion occurs makes the Generalized Alignment Index (GALI) method important. In this study, the chaoticity of Gursey instanton solutions was investigated by the Generalized Alignment Index (GALI) method.

References

  • Akdeniz KG, 1982. On classical solutions of Gursey’s conformal-invariant spinor model. Lettere al Nuovo Cimento, 33(2): 40–44.
  • Antonopoulos C, Bountis T, 2006. Detecting order and chaos by the linear dependence index method. Romai Journal, 2(2): 1-13.
  • Aydogmus F, Canbaz B, Onem C, Akdeniz KG, 2013. The behaviours of Gursey instantons in phase space. Acta Physica Polonica B, 44(9): 1837–1845.
  • Belitsky AV, Vandoren S, Van Nieuwenhuizen P, 2000. Yang-Mills and D-instantons. Classical and Quantum Gravity, 17(17): 3521-3570.
  • Christodoulidi H, Bountis T, 2006. Low-dimensional quasiperiodic motion in hamiltonian systems. Romai Journal 2(2): 37-44.
  • Gursey F, 1956. On a conform-invariant spinor wave equation. Il Nuovo Cimento, 3(5): 988–1006.
  • Heisenberg W, 1954. Zur quantentheorie nichtrenormierbarer wellengleichungen. Zeitschrift für Naturforschung A, 9, 292–303.
  • Kortel F, 1956. On some solutions of Gursey’s conformal-invariant spinor wave equation. Il Nuovo Cimento, 4, 210–215.
  • Manos T, Skokos C, Antonopoulos C, 2012. Probing the local dynamics of periodic orbits by the Generalized Alignment Index (GALI) method. International Journal of Bifurcation and Chaos, 22(9): 1250218.
  • Moges HT, 2020. Investigating Chaos by the Generalized Alignment Index (GALI) Method. University of Cape Town.
  • Olive D, Sciuto S, Crewther RJ, 1979. Instantons in field theory. La Rivista del Nuovo Cimento, 2(8): 1-117.
  • Paranjape M, 2018. The theory and applications of instanton calculations. Cambridge University Press, England.
  • Senyange B, Skokos C, 2022. Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method. Physica D: Nonlinear Phenomena, 432: 133154.
  • Shifman M, 1994. Instantons in gauge theories. World Scientific, Singapore.
  • Skokos C, Bountis T, Antonopoulos C, 2007. Geometrical properties of local dynamics in hamiltonian systems: the Generalized Alignment Index (GALI) method. Physica D, 231(1): 30-54.
  • Skokos C, Bountis T, Antonopoulos C, 2008. Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi-Pasta-Ulam lattices by the Generalized Alignment Index method. The European Physical Journal Special Topics, 165(1): 5-14.
There are 16 citations in total.

Details

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

Mine Ak 0000-0003-1131-5529

Early Pub Date May 31, 2022
Publication Date June 1, 2022
Submission Date December 26, 2021
Acceptance Date February 11, 2022
Published in Issue Year 2022 Volume: 12 Issue: 2

Cite

APA 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. https://doi.org/10.21597/jist.1047562
AMA Ak M. 4 Boyutlu Fermiyonik Modelde Kaosun Genelleştirilmiş Hizalama İndeksi Yöntemiyle İncelenmesi. J. Inst. Sci. and Tech. June 2022;12(2):726-734. doi:10.21597/jist.1047562
Chicago Ak, Mine. “4 Boyutlu Fermiyonik Modelde Kaosun Genelleştirilmiş Hizalama İndeksi Yöntemiyle İncelenmesi”. Journal of the Institute of Science and Technology 12, no. 2 (June 2022): 726-34. https://doi.org/10.21597/jist.1047562.
EndNote Ak M (June 1, 2022) 4 Boyutlu Fermiyonik Modelde Kaosun Genelleştirilmiş Hizalama İndeksi Yöntemiyle İncelenmesi. Journal of the Institute of Science and Technology 12 2 726–734.
IEEE M. Ak, “4 Boyutlu Fermiyonik Modelde Kaosun Genelleştirilmiş Hizalama İndeksi Yöntemiyle İncelenmesi”, J. Inst. Sci. and Tech., vol. 12, no. 2, pp. 726–734, 2022, doi: 10.21597/jist.1047562.
ISNAD Ak, Mine. “4 Boyutlu Fermiyonik Modelde Kaosun Genelleştirilmiş Hizalama İndeksi Yöntemiyle İncelenmesi”. Journal of the Institute of Science and Technology 12/2 (June 2022), 726-734. https://doi.org/10.21597/jist.1047562.
JAMA Ak M. 4 Boyutlu Fermiyonik Modelde Kaosun Genelleştirilmiş Hizalama İndeksi Yöntemiyle İncelenmesi. J. Inst. Sci. and Tech. 2022;12:726–734.
MLA Ak, Mine. “4 Boyutlu Fermiyonik Modelde Kaosun Genelleştirilmiş Hizalama İndeksi Yöntemiyle İncelenmesi”. Journal of the Institute of Science and Technology, vol. 12, no. 2, 2022, pp. 726-34, doi:10.21597/jist.1047562.
Vancouver Ak M. 4 Boyutlu Fermiyonik Modelde Kaosun Genelleştirilmiş Hizalama İndeksi Yöntemiyle İncelenmesi. J. Inst. Sci. and Tech. 2022;12(2):726-34.