  We use a recently obtained resummed quark propagator at finite temperature
which takes into account both the chromoelectric scale gT and the
chromomagnetic scale g^2T through the Gribov action. The electric scale
generates two massive modes whereas the magnetic scale produces a new massless
spacelike mode in the medium. Moreover, the non-perturbative quark propagator
is found to contain no discontinuity in contrast to the standard perturbative
hard thermal loop approach. Using this non-perturbative quark propagator and
self-consistent vertices, we compute the non-perturbative dilepton rate at
vanishing three-momentum at one-loop order. The resulting rate has a rich
structure at low energies due to the inclusion of the non-perturbative magnetic
scale. We also calculate the quark number susceptibility, which is related to
the conserved quark number density fluctuation in the deconfined state. Both
the dilepton rate and quark number susceptibility are compared with results
from lattice quantum chromodynamics and the standard hard thermal loop
approach. Finally, we discuss how the absence of a discontinuity in the
imaginary part of the non-perturbative quark propagator makes the results for
both dilepton production and quark number susceptibility dramatically different
from those in perturbative approaches and seemingly in conflict with known
lattice data.
