  We show that the period clustering of anomalous X-ray pulsars (AXPs) and soft
gamma-ray repeaters (SGRs), their X-ray luminosities, ages and statistics can
be explained with fallback disks with large initial specific angular momentum.
The disk evolution models are developed by comparison to self-similar
analytical models. The initial disk mass and angular momentum set the viscous
timescale. An efficient torque, with (1 - w^2) dependence on the fastness
parameter w leads to period clustering in the observed AXP-SGR period range
under a wide range of initial conditions. The timescale t_0 for the early
evolution of the fallback disk, and the final stages of fallback disk
evolution, when the disk becomes passive, are the crucial determinants of the
evolution. The disk becomes passive at temperatures around 100 K, which
provides a natural cutoff for the X-ray luminosity and defines the end of
evolution in the observable AXP and SGR phase. This low value for the minimum
temperature for active disk turbulence indicates that the fallback disks are
active up to a large radius greater than ~10^{12} cm. We find that transient
AXPs and SGRs are likely to be older than their persistent cousins. A fallback
disk with mass transfer rates corresponding to the low quiescent X-ray
luminosities of the transient sources in early evolutionary phases would have a
relatively lower initial mass, such that the mass-flow rate in the disk is not
sufficient for the inner disk to penetrate into the light cylinder of the young
neutron star, making mass accretion onto the neutron star impossible. The
transient AXP phase therefore must start later. The model results imply that
the transient AXP/SGRs, although older, are likely to be similar in number to
persistent sources (abridged).
