  This paper begins with an examination of the revival structure and long-term
evolution of Rydberg wave packets for hydrogen. We show that after the initial
cycle of collapse and fractional/full revivals, which occurs on the time scale
$t_{\rm rev}$, a new sequence of revivals begins. We find that the structure of
the new revivals is different from that of the fractional revivals. The new
revivals are characterized by periodicities in the motion of the wave packet
with periods that are fractions of the revival time scale $t_{\rm rev}$. These
long-term periodicities result in the autocorrelation function at times greater
than $t_{\rm rev}$ having a self-similar resemblance to its structure for times
less than $t_{\rm rev}$. The new sequence of revivals culminates with the
formation of a single wave packet that more closely resembles the initial wave
packet than does the full revival at time $t_{\rm rev}$, i.e., a superrevival
forms. Explicit examples of the superrevival structure for both circular and
radial wave packets are given. We then study wave packets in alkali-metal
atoms, which are typically used in experiments. The behavior of these packets
is affected by the presence of quantum defects that modify the hydrogenic
revival time scales and periodicities. Their behavior can be treated
analytically using supersymmetry-based quantum-defect theory. We illustrate our
results for alkali-metal atoms with explicit examples of the revival structure
for radial wave packets in rubidium.
