A new approach of chaos and complex network method to study fluctuation and phase transition in nuclear collision at high energy

Abstract

In the endeavour to study fluctuation and a signature of phase transition in ultrarelativistic nuclear collision during the process of particle production, an approach based on chaos and complex network is proposed. In this work we have attempted an exhaustive study of pion fluctuation in $\eta$ space, $\phi$ space, their cross-correlation and finally two-dimensional fluctuation in terms of scaling of void probability distribution. The analysis is done on the $\eta$ values and their corresponding $ \phi$ values extracted from the 32S-Ag/Br interaction at an incident energy of 200GeV per nucleon. The methods used are Multifractal Detrended Cross-Correlation Analysis (MF-DXA) and a chaos-based rigorous complex network method --Visibility Graph. The analysis reveals that the highest degree of cross-correlation between pseudorapidity and azimuthal angles exists in the most central region of the interaction. The analysis further shows that two-dimensional void distribution corresponding to the $\eta$ - $\phi$ space reveals a strong scaling behaviour. Both cross-correlation coefficients of MF-DXA and PSVG (Power of the Scale-freeness in Visibility Graph, which is implicitly connected with the Hurst exponent) can be effectively used for the quantitative assessment of pion fluctuation in a very precise manner and have the capability to assess the tendency of approaching criticality for phase transitions.