  Due to interest in both solid state based quantum computing architectures and
the application of quantum mechanical systems to nanomagnetometry, there has
been considerable recent attention focused on understanding the microscopic
dynamics of solid state spin baths and their effects on the coherence of a
controllable, coupled central electronic spin. Many analytic approaches are
based on simplified phenomenological models in which it is difficult to capture
much of the complex physics associated with this system. Conversely, numerical
approaches reproduce this complex behaviour, but are limited in the amount of
theoretical insight they can provide. Using a systematic approach based on the
spatial statistics of spin bath constituents, we develop a purely analytic
theory for the central spin decoherence problem of Nitrogen Vacancy centres in
diamond that reproduces the experimental and numerical results found in the
literature, whilst correcting a number of limitations and inaccuracies
associated with existing analytical approaches.
