  We use Brownian dynamics simulations of a binary mixture of highly charged
spherical colloidal particles to illustrate many of the implications of the
Random First Order Transition (RFOT) theory (PRA 40 1045 (1989)), which is the
only theory that provides a unified description of both the statics and
dynamics of the liquid to glass transition. In accord with the RFOT, we find
that as the volume fraction of the colloidal particles \f, the natural variable
that controls glass formation in colloidal systems, approaches \f_A there is an
effective ergodic to non-ergodic dynamical transition, which is signalled by a
dramatic slowing down of diffusion. In addition, using the energy metric we
show that the system becomes non-ergodic as \f_A is approached. The time t^*,
at which the four-point dynamical susceptibility achieves a maximum, also
diverges near \f_A. Remarkably, three independent measures(translational
diffusion coefficients, ergodic diffusion coefficients,as well t^*) all signal
that at \f_A=0.1 ergodicity is effectively broken. The translation diffusion
constant, the ergodic diffusion constant, and (t^*)^-1 all vanish as
(\f_A-\f)^g with both \f_A and g being the roughly the same for all three
quantities. Below \f_A transport involves crossing suitable free energy
barriers. In this regime, the density-density correlation function decays as a
stretched exponential exp(-t/tau_a)^b with b=0.45. The \f-dependence of the
relaxation time \tau_a is well fit using the VFT law with the ideal glass
transition occurring at \f_K=0.47. By using an approximate measure of the local
entropy (s_3) we show that below \f_A the law of large numbers, which states
that the distribution of s_3 for a large subsample should be identical to the
whole sample, is not obeyed. The comprehensive analyses provided here for
Wigner glass forming charged colloidal suspensions fully validate the concepts
of the RFOT.
