  There appears to be a longtime, very slowly evolving state in dense simple
fluids which, for high enough density, approaches a glassy nonergodic state.
The nature of the nonergodic state can be characterized by the associated
static equilibrium state. In particular, systems driven by Smoluchowski or
Newtonian dynamics share the same static equilibrium and nonergodic states.
That these systems share the same nonergodic states is a highly nontrivial
statement and requires establishing a number of results. In the high-density
regime one finds that an equilibrating system decays via a three-step process
identified in mode-coupling theory (MCT). For densities greater than a critical
density one has time-power-law decay with exponents a and b. There are sets of
linear fluctuation dissipation relations (FDRs) which connect the cumulants of
these two fields. The form of the FDRs is the same for both Smoluchowski or
Newtonian dynamics. While we show this universality of nonergodic states within
perturbation theory, we expect it to be true more generally.
  The nature of the approach to the nonergodic state has been suggested by MCT.
It has been a point of contention that MCT is a phenomenological theory and not
a systematic theory with prospects for improvement. Recently a systematic
theory has been developed. It naturally allows one to calculate
self-consistently density cumulants in a perturbation expansion in a
pseudo-potential. At leading order one obtains a kinetic kernel quadratic in
the density. This is a "one-loop" theory like MCT. At this one-loop level one
finds vertex corrections which depend on the three-point equilibrium cumulants.
Here we assume these vertex-corrections can be ignored and focus on the
higher-order loops. We show that one can sum up all of the loop contributions.
The higher-order loops do not change the nonergodic state parameters
substantially.
