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This chapter describes the relationship between low frequency noise andcoherence decay of localized spins in semiconductors. Section 2 establishes adirect relationship between an arbitrary noise spectral function and spincoherence as measured by a number of pulse spin resonance sequences. Section 3describes the electron-nuclear spin Hamiltonian, including isotropic andanisotropic hyperfine interactions, inter-nuclear dipolar interactions, and theeffective Hamiltonian for nuclear-nuclear coupling mediated by the electronspin hyperfine interaction. Section 4 describes a microscopic calculation ofthe nuclear spin noise spectrum arising due to nuclear spin dipolar flip-flopswith quasiparticle broadening included. Section 5 compares our explicitnumerical results to electron spin echo decay experiments for phosphorus dopedsilicon in natural and nuclear spin enriched samples.Comment: Book chapter in "Electron spin resonance and related phenomena in low  dimensional structures", edited by Marco Fanciulli. To be published by  Springer-Verlag in the TAP series. 35 pages, 9 figure

Electron Spin as a Spectrometer of Nuclear-Spin Noise and Other Fluctuations