# Pion Fluctuation in High-energy Collisions --- A Chaos-based Quantitative Estimation with Visibility Graph Technique

Bhaduri, Susmita (Deepa Ghosh Research Foundation, 60/7/1, Maharaja Tagore Road, Kolkata-700031, India) ; Ghosh, Dipak (Deepa Ghosh Research Foundation, 60/7/1, Maharaja Tagore Road, Kolkata-700031, India)

16 May 2017

Abstract: We propose a new approach for studying pion fluctuation for deeper understanding of the internal dynamics, from a perspective of fractional Brownian motion (fBm)-based complex network analysis method called Visibility Graph analysis. This chaos-based, rigorous, non-linear technique is applied to study the erratic behaviour of multipion production in $\pi^{-}$--Ag/Br interactions at 350~GeV. This method can offer reliable results with finite data points. The Power of Scale-freeness of Visibility Graph denoted by PSVG is a measure of fractality, which can be used as a quantitative parameter for the assessment of the state of a chaotic system. The event-wise fluctuation of the multipion production process can be represented by this parameter. From the analysis of the PSVG, we can quantitatively confirm that fractal behaviour of the particle production process depends on the target excitation, and the fractality decreases with the increase of target excitation.

Published in: Acta Physica Polonica B 48 (2017) 741-755