Correlations among proton collective flows in Au + Au collisions at $E_{beam} = 1.23$$A$ GeV within the isospin-dependent quantum molecular dynamics model

摘要: We simulated proton collective flows in Au + Au collisions at a beam energy of 1.23$A$ GeV using the isospin-dependent quantum molecular dynamics (IQMD) model. We applied the event-plane method to calculate the first- to fourth-order flow coefficients in different $v_2$ classes,  studying the correlations among them. Nearly all event classes satisfy the scaling relation $v_3\propto v_{1}v_{2}$. Quadrangular flow $v_4$ also approximately follows the scaling relation $v_4 = 0.5 v_2^2$. Additionally, we calculated the Pearson correlation coefficients between the first to fourth harmonic flows for protons, thereby quantifying the inter-harmonic correlations. The Pearson linear correlation coefficient $corr(v_{n},\varepsilon_{n})$ between each flow harmonic and the corresponding eccentricity under different centralities is also examined.