Non-Markovian Dynamics of a Localized Electron Spin Due to the Hyperfine Interaction

We review our theoretical work on the dynamics of a localized electron spin interacting with an environment of nuclear spins. Our perturbative calculation is valid for arbitrary polarization p of the nuclear spin system and arbitrary nuclear spin I in a sufficiently large magnetic field. In general, the electron spin shows rich dynamics, described by a sum of contributions with exponential decay, nonexponential decay, and undamped oscillations. We have found an abrupt crossover in the long-time spin dynamics at a critical shape and dimensionality of the electron envelope wave function. We conclude with a discussion of our proposed scheme to measure the relevant dynamics using a standard spin-echo technique.