  Ensembles of alkali or noble-gas atoms at room temperature and above are
widely applied in quantum optics and metrology owing to their long-lived spins.
Their collective spin states maintain nonclassical nonlocal correlations,
despite the atomic thermal motion in the bulk and at the boundaries. Here we
present a stochastic, fully-quantum description of the effect of atomic
diffusion in these systems. We employ the Bloch-Heisenberg-Langevin formalism
to account for the quantum noise originating from diffusion and from various
boundary conditions corresponding to typical wall coatings, thus modeling the
dynamics of nonclassical spin states with spatial inter-atomic correlations. As
examples, we apply the model to calculate spin noise spectroscopy, temporal
relaxation of squeezed spin states, and the coherent coupling between two spin
species in a hybrid system.
