  We generalize the two-channel (Edwards) fermion-boson model describing
quantum transport in a background medium to the more realistic case of
dispersive bosons. Using the variational exact diagonalization technique, we
numerically solve the extended model in a one-dimensional setting, for both
downward and upward curved boson dispersion, and show that going away from the
previous Einstein-boson assumption has profound consequences for the particle
transport. Specifically, we analyze the ground-state and spectral properties
and demonstrate the renormalization of the particle's coherent band, effective
mass, photoemission spectra and fermion-boson correlation functions due to the
interplay of fluctuations and correlations in a dispersive environment.
