  The relationship between chaos and quantum mechanics has been somewhat uneasy
-- even stormy, in the minds of some people. However, much of the confusion may
stem from inappropriate comparisons using formal analyses. In contrast, our
starting point here is that a complete dynamical description requires a full
understanding of the evolution of measured systems, necessary to explain actual
experimental results. This is of course true, both classically and quantum
mechanically. Because the evolution of the physical state is now conditioned on
measurement results, the dynamics of such systems is intrinsically nonlinear
even at the level of distribution functions. Due to this feature, the
physically more complete treatment reveals the existence of dynamical regimes
-- such as chaos -- that have no direct counterpart in the linear (unobserved)
case. Moreover, this treatment allows for understanding how an effective
classical behavior can result from the dynamics of an observed quantum system,
both at the level of trajectories as well as distribution functions. Finally,
we have the striking prediction that time-series from measured quantum systems
can be chaotic far from the classical regime, with Lyapunov exponents differing
from their classical values. These predictions can be tested in next-generation
experiments.
