BİKROMATİK POTANSİYELİN THIRRING İNSTANTONLARI ÜZERINE ETKİSİ

Year 2017, Volume: 19 Issue: 55, 258 - 266, 01.01.2017

Fatma Aydogmus

Abstract

Thirring model iki boyutlu konformal invaryant kütlesiz saf bir fermiyonik modeldir. Model parçacık benzeri çözümler sergiler ve bu çözümler instanton karakterindedir. Bu çalışmada Thirring instantonlarının lineer olmayan dinamiğini daha iyi kavrayabilmek için bikromatik potansiyelin model üzerindeki etkisi incelenmiştir. Bu amaçla faz portreleri inşa edilmiş ve bazı sistem parametre değerleri için kaos gözlemlenmiştir

Keywords

Soliton , İnstanton , Bikromatik , Lineer olmayan dinamik.

Bikromatik Potansiyelin Thirring İnstantonları Üzerine Etkisi

Abstract

Thirring model iki boyutlu konformal invaryant kütlesiz saf bir fermiyonik modeldir. Model parçacık benzeri çözümler sergiler ve bu çözümler instanton karakterindedir. Bu çalışmada Thirring instantonlarının lineer olmayan dinamiğini daha iyi kavrayabilmek için bikromatik potansiyelin model üzerindeki etkisi incelenmiştir. Bu amaçla faz portreleri inşa edilmiş ve bazı sistem parametre değerleri için kaos gözlemlenmiştir

Keywords

Soliton , Instanton , Bichromatic , Nonlinear dynamic.

References

• [1] Louis de Broglie, An Introduction to the Study of Wave Mechanics, London, Methuen and Co.Ltd, 1930.
• [2] M. Dunajski, Solitons, Instantons, and Twistors, Oxford University Press, New York 2010.
• [3] C. Rebbi and G. Solliani, Solitons and Particles, World Scientific, 1984; T. Dauoxois and M. Peyrard, Physics of Solitons, Cambridge University Press, 2006.
• [4] C.Houghton, Instantons, in the Encyclopaedia of Nonlinear Science, Routledge, New York, 2005.
• [5] ] R. Rajaraman, Solitons and Instantons, North-Holland, Elsevier Science Publisher, 1982.
• [6] M. Kuhlen, QCD at HERA: The Hadronic Final State in Deep Inelastic Scattering, SpringerVarlag Berlin, 1998.
• [7] M. Eto and M. Nitta, Semilocal fractional instantons, Journal of High Energy Physics, 67, 2016, pp.1-19
• [8] S. Moch, A. Ringwald, and F. Schrempp, Instantons in Deepinelastic Scattering: The Simplest Process, Nucl. Phys., B507, 1997, pp.134-156
• [9] A. Ringwald and F. Schrempp, Instanton-induced Cross-sections in Deep-inelastic Scattering, Phys. Lett.,B438, 1998, pp.217-228.
• [10] F.Schrempp and A. Ringwald, Zooming-in on Instantons at HERA, Phys.Lett. B503, 2001, pp.331-340.
• [11] A. Ringwald and F. Schrempp, Qcdins2.0: A Montecarlo Generator for Instanton induced Processes in Deep-inelastic Scattering, Comput. Phys. Commun., 132, 2000, pp. 267 305.
• [12] F. Kortel, On some solutions of Gursey’s conformal-invariant spinor wave equation, Il Nuovo Cimento, 4, 1956, pp.210-215
• [13] K.G. Akdeniz and A. Smailagic, Classical Solitons for Fermionic Models, Il Nuovo Cimento, 51A, 1979, pp.345-357.
• [14] F. Aydogmus, The Behaviours of Spinor Type Instanton Attractors in Phase Space, Istanbul University, Institute of Science, Physics Department Ph.D. Thesis, 2012).
• [15] B. Canbaz, C. Onem, F. Aydogmus and K. G. Akdeniz, From Heisenberg Ansatz to Attractor of Thirring Instanton, Chaos Solitons& Fractals, 45, 2012, pp. 188-191.
• [16] F. Aydogmus and E. Tosyali, Common Behaviours of Spinor Type Instantons in 2-D Thirring and 4-D Gursey Fermionic Models, Advances in High Energy Physics, 148375 2014, pp.1-11
• [17] F. Bruckmann, Instanton Constituents in the O(3) Model at Finite Temeperature, Phys. Rev. Lett. 100, 051602, 2008, pp.1-4.
• [18] W. Brendel, F. Bruckmann, L. Janssen, A. Wipf and C. Wozar, Instanton Constituents and Fermionic Zero Modes in Twisted CP(n) Models, Phys. Lett. B 676, 116, 2009, pp.116-125.
• [19] M. Nitta and W. Vinci, Decomposing Instantons in Two Dimensions, J. Phys. A, 45, 17, 2012, pp.1-23.
• [20] G. V. Dunne and M. Unsal, Uniform WKB, Multi-instantons and Resurgent Trans-Series, Phys. Rev.D 89, 105009, 2014, pp.1-22.
• [21] M. Nitta, Fractional Instantons and Bions in the O(N) Model with Twisted Boundary Conditions, Journal of High Energy Physics 37, 108, 2015, pp.1-37.
• [22] W. E. Thirring, A Soluble Relativistic Field Theory, Anal Physics, 3, 1958, pp. 91-112). [23] W. Heisenberg, Zeits. F. Naturf. A9,1954, 292
• [24] S. Strogatz, Nonlinear Dynamics and Chaos:With Applications to Physics, Biology, Chemistry, and Engineering, PerseusBooks, 1999.
• [25] G. Duffing, Erzwungene Schwingungenbei Veranderlicher Eigenfrequenz., F. Vieweg u. Sohn, Braunschweig, 1918.
• [26] A.N. Kolmogorov, On the Conservation of Conditionally Periodic Motions under Small Perturbation of the Hamiltonian, Dokl. akad. nauk SSSR, vol. 98, 1954, pp.527–530, Engl.10 transl.: Stochastic Behaviour in Classical and Quantum Hamiltonian Systems, Volta Memorial conference, 1977, Lecture Notes in Physics, 93, Springer, 1979, pp.51–56, Arnold, V. I., Russ. Math. Surv., 18, 13, 1963, Moser, J., Nachr. Akad. Wiss. Gött. II, 1, 1962.
• [27] F. Aydogmus and E. Tosyali, Numerical Analysis of Thirring Model under White Noise, Journal of Physics: Conference Series 633, 012022, 2015, pp.1-4
• [28] F. Aydogmus, Chaos in a 4D Dissipative Nonlinear Fermionic Model, Journal of Modern Physics C, 26, 7, 1550083, 2015, pp.1-13.
• [29] F. Aydogmus, Unstable Behaviours of Classical Solutions in Spinor-type Conformal Invariant Fermionic Models, arXiv:1508.00610 [hep-th], 2015