Investigation of Nonlinear Collective Dynamics in Relativistic Heavy-Ion Collisions Using A Multi-Phase Transport Model

Abstract

The nonlinear response coefficient, $χ_{4,22}$, is a crucial observable for probing the dynamical properties of the quark-gluon plasma (QGP). Although traditionally interpreted as a signature of medium response, recent studies suggest that $χ_{4,22}$ also encodes information about the intrinsic initial-state configuration of the colliding nuclei. In this study, we use the A Multi-Phase Transport (AMPT) model to investigate the microscopic origin and stage-by-stage development of $χ_{4,22}$ in $^{238}$U+$^{238}$U and $^{197}$Au+$^{197}$Au collisions at $\sqrt{s_{\rm NN}} = 200$ GeV. By tracking flow observables through the partonic cascade, quark coalescence, and hadronic rescattering phases, we map the conversion of initial geometric eccentricities into final-state momentum anisotropies. Our results demonstrate that the absolute magnitude of $χ_{4,22}$ increases continuously during collective expansion, confirming its nature as a dynamically generated medium response. In contrast, the relative ratio of this coefficient between the U+U and Au+Au systems, $R(χ_{4,22})$, exhibits approximate stage independence over a broad centrality range, as quantified by a constant-fit test across the three AMPT evolution stages. This indicates that the ratio reduces common medium-response effects, such as overall amplification efficiency and viscous attenuation, and therefore retains stronger sensitivity to the relative initial-state geometry. These findings provide theoretical support for using nonlinear flow ratios to constrain higher-order nuclear structure, such as hexadecapole deformation, while also clarifying the residual stage dependence and nonflow limitations relevant to precision extractions.