In a quasi-particle model of QCD matter at finite temperature with thermal masses for quarks and gluons from hard thermal loops, the equation of state (EOS) can be described by an effective temperature dependence of the strong coupling g(T). Assuming the same effective coupling between the exchanged gluon and thermal partons, the EOS can also be related to parton energy loss. Based on the quasi-particle linear Boltzmann transport (QLBT) model coupled to a (3+1)-dimensional viscous hydrodynamic model of the quark-gluon plasma (QGP) evolution and a hybrid fragmentation-coalescence model for heavy quark hadronization, we perform a Bayesian analysis of the experimental data on D meson suppression RAA and anisotropy v2 at RHIC and the LHC. We achieve a simultaneous constraint on the QGP EOS and the heavy quark transport coefficient, both consistent with the lattice QCD results.

Within an advanced Langevin-hydrodynamics framework coupled to a hybrid fragmentation-coalescence hadronization model, we study heavy flavor quenching and flow in relativistic heavy-ion collisions. We investigate how the initial heavy quark spectrum, the in-medium energy loss and hadronization mechanisms of heavy quarks, the evolution profile of the pre-equilibrium stage, the medium flow, and the temperature dependence of heavy quark diffusion coefficients influence the suppression and elliptic flow of heavy mesons at the RHIC and the LHC. Our results show that the different modeling of initial conditions, pre-equilibrium evolution, and in-medium interactions can individually yield uncertainties of approximately 10-40% in D meson suppression and flow at a low transverse momentum. We also find that proper combinations of collisional versus radiative energy loss, coalescence versus fragmentation in hadronization, and the inclusion of medium flow are the most important factors for describing the suppression and elliptic flow of heavy mesons.

We develop a new heavy quark transport model, QLBT, to simulate the dynamical propagation of heavy quarks inside the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. Our QLBT model is based on the linear Boltzmann transport (LBT) model with the ideal QGP replaced by a collection of quasi-particles to account for the non-perturbative interactions among quarks and gluons of the hot QGP. The thermal masses of quasi-particles are fitted to the equation of state from lattice QCD simulations using the Bayesian statistical analysis method. Combining QLBT with our advanced hybrid fragmentation-coalescence hadronization approach, we calculate the nuclear modification factor RAA and the elliptic flow v2 of D mesons at the Relativistic Heavy-Ion Collider and the Large Hadron Collider. By comparing our QLBT calculation to the experimental data on the D meson RAA and v2, we extract the heavy quark transport parameter q^ and diffusion coefficient Ds in the temperature range of 1-4Tc, and compare them with the lattice QCD results and other phenomenological studies.