  The topography of the free energy landscape in phase space of a dense hard
sphere system characterized by a discretized free energy functional of the
Ramakrishnan-Yussouff form is investigated numerically using a
``microcanonical'' Monte Carlo procedure. We locate a considerable number of
glassy local minima of the free energy and analyze the distributions of the
free energy at a minimum and an appropriately defined phase-space ``distance''
between different minima. We find evidence for the existence of pairs of
closely related glassy minima (``two-level systems''). We also investigate the
way the system makes transitions as it moves from the basin of attraction of a
minimum to that of another one after a start under nonequilibrium conditions.
This allows us to determine the effective height of free energy barriers that
separate a glassy minimum from the others. The dependence of the height of free
energy barriers on the density is investigated in detail. The general
appearance of the free energy landscape resembles that of a putting green:
relatively deep minima separated by a fairly flat structure. We discuss the
connection of our results with the Vogel-Fulcher law and relate our
observations to other work on the glass transition.
