  We study the influence of narrowed distributions of the nuclear Overhauser
field on the decoherence of a central electron spin in quantum dots. We
describe the spin dynamics in quantum dots by the central spin model. We use
analytic solutions for uniform couplings and the time dependent density-matrix
renormalization group (tDMRG) for nonuniform couplings. With these tools we
calculate the dynamics of the central spin for large baths of nuclear spins
with or without external magnetic field applied to the central spin. The focus
of our study is the influence of initial mixtures with narrowed distributions
of the Overhauser field and of applied magnetic fields on the decoherence of
the central spin.
