  We present a method to characterize non-Abelian anyons that is based only on
static measurements and that does not rely on any form of interference. For
geometries where the anyonic statistics can be revealed by rigid rotations of
the anyons, we link this property to the angular momentum of the initial state.
We test our method on the paradigmatic example of the Moore-Read state, that is
known to support excitations with non-Abelian statistics of Ising type. As an
example, we reveal the presence of different fusion channels for two such
excitations, a defining feature of non-Abelian anyons. This is obtained by
measuring density-profile properties, like the mean square radius of the system
or the depletion generated by the anyons. Our study paves the way to novel
methods for characterizing non-Abelian anyons, both in the experimental and
theoretical domains.
