We theoretically study a Josephson junction based on a semiconducting
nanowire subject to a time-dependent flux bias. We establish a general density
matrix approach for the dynamical response of the Majorana junction and
calculate the resulting flux-dependent susceptibility using both microscopic
and effective low-energy descriptions for the nanowire. We find that the
diagonal component of the susceptibility, associated with the dynamics of the
Majorana states populations, dominates over the standard Kubo contribution for
a wide range of experimentally relevant parameters. The diagonal term, thus far
unexplored in the context of Majorana physics, allows to probe accurately the
presence of Majorana bound states in the junction.Comment: 5 pages, 3 figures, 15 pages of supplemental materia