Quantum spin dynamics of heavy quarks and polarization observables in relativistic heavy-ion collisions

We develop a quantum spin-density-matrix framework for heavy-quark spin dynamics in relativistic heavy-ion collisions. Starting from an initial polarization induced along the magnetic-field direction, we derive the evolution equation for spin polarization within this framework and obtain analytic solutions. The evolved polarization is connected to open heavy-flavor observables via a fragmentation-based hadronization prescription. For vector mesons, the spin-alignment parameter $\rho_{00}$ is constructed by coupling the heavy-quark spin to that of the light antiquark produced during fragmentation. We confront our results with recent ALICE measurements of prompt $D^{*+}$ spin alignment in Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02~{\rm TeV}$ and extract an effective depolarization strength that determines the spin-relaxation time scale. Using this fitted parameter, we provide benchmark estimates for $\Lambda_c^+$ and $\bar{\Lambda}_c^-$ polarization, up to an overall spin-transfer normalization. We further estimate the recently proposed elliptic polarization harmonic arising from path-length-dependent depolarization in an anisotropic fireball.