  We study the chiral anomaly in disordered Weyl semimetals, where the broken
translational symmetry prevents the direct application of Nielsen and
Ninomiya's mechanism and disorder is strong enough that quantum effects are
important. In the weak disorder regime, there exist rare regions of the random
potential where the disorder strength is locally strong, which gives rise to
quasilocalized resonances and their effect on the chiral anomaly is unknown. We
numerically show that these resonant states do not affect the chiral anomaly
only in the case of a single Weyl node. At energies away from the Weyl point,
or with strong disorder where one is deep in the diffusive regime, the chiral
Landau level itself is not well defined and the semiclassical treatment is not
justified. In this limit, we analytically use the supersymmetry method and find
that the Chern-Simons term in the effective action which is not present in
nontopological systems gives rise to a nonzero average level velocity which
implies chiral charge pumping. We numerically establish that the nonzero
average level velocity serves as an indicator of the chiral anomaly in the
diffusive limit.
