  We study the collective motion of atoms confined in an optical lattice
operating inside a high finesse ring cavity. A simplified theoretical model for
the dynamics of the system is developed upon the assumption of adiabaticity of
the atomic motion. We show that in a regime where the light shift per photon
times the number of atoms exceeds the line width of the cavity resonance, the
otherwise tiny retro-action of the atoms upon the light field becomes a
significant feature of the system, giving rise to dispersive optical
bistability of the intra-cavity field. A solution of the complete set of
classical equations of motion confirms these finding, however additional
non-adiabatic phenomena are predicted, as for example self-induced radial
breathing oscillations. We compare these results with experiments involving
laser-cooled 85Rb atoms trapped in an optical lattice inside a ring cavity with
a finesse of 180000. Temperature measurements conducted for moderate values of
the atom-cavity interaction demonstrate that intensity-noise induced heating is
kept at a very low level, a prerequisite for our further experiments. When we
operate at large values of the atom--cavity interaction we observe bistability
and breathing oscillations in excellent agreement with our theoretical
predictions.
