  This chapter describes the relationship between low frequency noise and
coherence decay of localized spins in semiconductors. Section 2 establishes a
direct relationship between an arbitrary noise spectral function and spin
coherence as measured by a number of pulse spin resonance sequences. Section 3
describes the electron-nuclear spin Hamiltonian, including isotropic and
anisotropic hyperfine interactions, inter-nuclear dipolar interactions, and the
effective Hamiltonian for nuclear-nuclear coupling mediated by the electron
spin hyperfine interaction. Section 4 describes a microscopic calculation of
the nuclear spin noise spectrum arising due to nuclear spin dipolar flip-flops
with quasiparticle broadening included. Section 5 compares our explicit
numerical results to electron spin echo decay experiments for phosphorus doped
silicon in natural and nuclear spin enriched samples.
