Electron spin dynamics due to the hyperfine interaction

We investigate the influence of the Hyperfine interaction on the spin dynamics of the electrons in GaAs quantum dots formed by laterally patterned gates. To do this, we develop the density matrix formalism which treats the nuclear spins in a quantum statistical way. We use Laplace transforms to solve the master equations for the evolution of the three components of the ensemble-averaged electron spin in real time. We determine the dependence of the spin precession for several parameter values such as the temperature of the nuclei, the hyperfine coupling, the density of the nuclei and applied magnetic field. We find interesting interplay between the Overhauser field and the applied field.