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We extend the kinetic theory of $D$ mesons to accommodate thermal andoff-shell effects due to the medium modification of the heavy-meson spectralfunctions. From the Kadanoff-Baym approach we derive the off-shellFokker-Planck equation which encodes the heavy-flavor transport coefficients.We analyze the thermal width (damping rate) of $D$ mesons due to theirscattering off light mesons, focusing on new in-medium effects: off-shellcorrections, inelastic channels, and the contribution of the Landau cut. Weobtain that the latter effect (absent for vacuum scattering amplitudes) bringssizable corrections at moderate temperatures. We discuss how the heavy-flavortransport coefficients, like the drag and diffusion coefficients, are modifiedin matter. We find that the $D$-meson spatial diffusion coefficient matchessmoothly to the latest results of lattice-QCD calculations and Bayesiananalyses at higher temperatures.

In-medium kinetic theory of $D$ mesons and heavy-flavor transport coefficients