  We discuss a general and efficient approach for "bootstrapping" short-time
correlation data in chaotic or complex quantum systems to obtain information
about long-time dynamics and stationary properties, such as the local density
of states. When the short-time data is sufficient to identify an individual
quantum system, we obtain a systematic approximation for the spectrum and wave
functions. Otherwise, we obtain statistical properties, including wave function
intensity distributions, for an ensemble of all quantum systems sharing the
given short-time correlations. The results are valid for open or closed
systems, and are stable under perturbation of the short-time input data.
Numerical examples include quantum maps and two-dimensional anharmonic
oscillators.
