Fermiyon Benzeri İnstanton Çözümlerinin Dalgacık Entropi Analizinin İncelenmesi

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.

Anahtar Kelimeler:

Dalgacık dönüşümü, Faz uzayı, Fermiyon benzeri instanton, Dalgacık entropisi

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

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.

Keywords:

Wavelet transform, Phase space, Fermion-like instanton, Wavelet entropy,

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