By means of molecular dynamics simulations, we study the stationary points of
the potential energy in a Lennard-Jones liquid, giving a purely geometric
characterization of the energy landscape of the system. We find a linear
relation between the degree of instability of the stationary points and their
potential energy, and we locate the energy where the instability vanishes. This
threshold energy marks the border between saddle-dominated and minima-dominated
regions of the energy landscape. The temperature where the potential energy of
the Stillinger-Weber minima becomes equal to the threshold energy turns out to
be very close to the mode-coupling transition temperature.Comment: Invited talk presented by A.C. at the Conference: Disordered and
Complex Systems, King's College London, July 200
