  In this work, we consider decoherence of a central spin by a spin bath. In
order to study the non-perturbative decoherence regimes, we develop an
efficient mean-field-based method for modeling the spin-bath decoherence, based
on the P-representation of the central spin density matrix. The method can be
applied to longitudinal and transversal relaxation at different external
fields. In particular, by modeling large-size quantum systems (up to 16000 bath
spins), we make controlled predictions for the slow long-time decoherence of
the central spin.
