In chemical physics, the energy landscape (the energy as a function of
the coordinates of all the atoms) of a system is often characterized to
try to understand the beahviour of a system, be it a cluster,
biomolecule, supercooled liquid, ... For example, the ability of
proteins to find their native structure has been ascribed to the
funnel-like topography of the energy landscape, which guides unfolded
proteins down towards the functionally active state. In this talk I
look at some of the fundamental properties of energy landscapes.
Somewhat surprisingly, I have found that the network of connections
between states on the landscape is "scale-free"
and that the basins of attraction surrounding the minima on the
landscape form a fractal Apollonian-like packing of configuration