  Extremely large angular orbital momentum can be produced in non-central
heavy-ion collisions, leading to a strong transverse polarization of partons
that scatter through the quark-gluon plasma (QGP) due to spin-orbital coupling.
We develop a perturbative approach to describe the formation and spacetime
evolution of quark polarization inside the QGP. Polarization from both the
initial hard scatterings and interactions with the QGP have been consistently
described using the quark-potential scattering approach, which has been coupled
to realistic initial condition calculation and the subsequent (3+1)-dimensional
viscous hydrodynamic simulation of the QGP for the first time. Within this
improved approach, we have found that different spacetime-rapidity-dependent
initial energy density distributions generate different time evolution profiles
of the longitudinal flow velocity gradient of the QGP, which further lead to an
approximately 15% difference in the final polarization of quarks collected on
the hadronization hypersurface of the QGP. Therefore, in addition to the
collective flow coefficients, the hyperon polarization may serve as a novel
tool to help constrain the initial condition of the hot nuclear matter created
in high-energy nuclear collisions.
