Survival rate of initial azimuthal anisotropy in a multi-phase transport model

We investigate the survival rate of an initial momentum anisotropy (${v}_2^{ini}$), not spatial anisotropy, to the final state in a multi-phase transport (AMPT) model in Au+Au collisions at $\sqrt{s_{NN}}$=200~GeV. It is found that both the final-state parton and charged hadron $v_2$ show a linear dependence versus $v_2^{ini}\{\rm PP\}$ with respect to the participant plane (PP). It is found that the slope of this linear dependence (referred to as the survive rate) increases with transverse momentum ($p_T$), reaching~$\sim$100\% at $p_T$$\sim$2.5 GeV/c for both parton and charged hadron. The survival rate decreases with collision centrality and energy, indicating decreasing survival rate with increasing interactions. It is further found that a $v_2^{ini}\{\rm Rnd\}$ with respect to a random direction does not survive in $v_2\{\rm PP\}$ but in the two-particle cumulant $v_2\{2\}$. The dependence of $v_2\{2\}$ on $v_2^{ini}\{\rm Rnd\}$ is quadratic rather than linear.