  The dynamics and decoherence of an electronic spin-1/2 qubit coupled to a
bath of nuclear spins via hyperfine interactions in a quantum dot is studied.
We show how exact results from the integrable solution can be used to
understand the dynamic behavior of the qubit. It is possible to predict the
main frequency contributions and their broadening for relatively general
initial states analytically, leading to an estimate of the corresponding decay
times. Furthermore, for a small bath polarization, a new low-frequency time
scale is observed.
