  Dynamic autocorrelations $<S_i^{\alpha}(t) S_i^{\alpha}>$ (\alpha=x,z) of an
isolated impurity spin in a S=1/2 XX chain are calculated. The impurity spin,
defined by a local change in the nearest-neighbor coupling, is either in the
bulk or at the boundary of the open-ended chain. The exact numerical
calculation of the correlations employs the Jordan-Wigner mapping from spin
operators to Fermi operators; effects of finite system size can be eliminated.
Two distinct temperature regimes are observed in the long-time asymptotic
behavior. At T=0 only power laws are present. At high T the x correlation
decays exponentially (except at short times) while the z correlation still
shows an asymptotic power law (different from the one at T=0) after an
intermediate exponential phase. The boundary impurity correlations follow power
laws at all T. The power laws for the z correlation and the boundary
correlations can be deduced from the impurity-induced changes in the properties
of the Jordan-Wigner fermion states.
