  We study the decoherence of a single electron spin in an isolated quantum dot
induced by hyperfine interaction with nuclei for times smaller than the nuclear
spin relaxation time. The decay is caused by the spatial variation of the
electron envelope wave function within the dot, leading to a non-uniform
hyperfine coupling.
  We evaluate the spin correlation function with and without magnetic fields
and find that the decay of the spin precession amplitude is not exponential but
rather power (inverse logarithm) law-like. For fully polarized nuclei we find
an exact solution and show that the precession amplitude and the decay behavior
can be tuned by the magnetic field.
  The corresponding decay time is given by $\hbar N/A$, where $A$ is a
hyperfine interaction constant and $N$ the number of nuclei inside the dot. The
amplitude of precession, reached as a result of the decay, is finite. We show
that there is a striking difference between the decoherence time for a single
dot and the dephasing time for an ensemble of dots.
