  A long-standing problem of the low-energy dynamics of a disordered XY spin
chain is re-examined. The case of a rigid chain is studied where the quantum
effects can be treated quasiclassically. It is shown that as the frequency
decreases, the relevant excitations change from localized spin waves to
two-level systems to soliton-antisoliton pairs. The linear-response correlation
functions are calculated. The results apply to other periodic glassy systems
such as pinned density waves, planar vortex lattices, stripes, and disordered
Luttinger liquids.
