Fractal structure of Christ-Lee model

Boming Zhang; Yunguo Jiang

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arXiv · 2503.20799

Fractal structure of Christ-Lee model

Boming Zhang·Yunguo Jiang

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Abstract

This paper numerically investigates the dynamical properties of kink and antikink collisions in the Christ_Lee model in the regime of epsilon approaching the phi4 theory. With given epsilon and the initial velocity Vin, we exhibiting the formation of bion, scattering, and n_bounce states. Additionally, we show the self_similar fractal structures in the plot of Vout_Vin with given epsilon. Specially, we find the fractal structure in the plot of Vout versus epsilon, which is not reported previously. We computes the Box_counting dimension for these fractal structures. We find that the Box_dimension is positively correlated with epsilon, and approaches to Hausdorff dimension of the Sierpinski triangle when epsilon is sufficiently large.

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Boming Zhang, Yunguo Jiang. 2025-03-23. Fractal structure of Christ-Lee model. https://arxiv.org/abs/2503.20799

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