  Evolution of the z-component of a single spin in the finite cyclic XY spin
1/2 chain is studied. Initially one selected spin is polarized while other
spins are completely unpolarized and uncorrelated. Polarization of the selected
spin as a function of time is proportional to the autocorrelation function at
infinite temperature. Initialization of the selected spin gives rise to two
wave packets moving in opposite directions and winding over the circle. We
express the correlation function as a series in winding number and derive
tractable approximations for each term. This allows to give qualitative
explanation and quantitative description to various finite-size effects such as
partial revivals and transition from regular to erratic behavior.
