  We study chiral fermions electroweakly interacting with a background matter
having the nonuniform density and the velocity arbitrarily depending on
coordinates. The dynamics of this system is described approximately by finding
the Berry phase. The effective action and the kinetic equations for right and
left particles are derived. In the case of a rotating matter, we obtain the
correction to the anomalous electric current and to the Adler anomaly. Then we
study some astrophysical applications. Assuming that the chiral imbalance in a
rotating neutron star vanishes, we obtain the rate of the magnetic helicity
change owing to the interaction of chiral electrons with background neutrons.
The characteristic time of the helicity change turns out to coincide with the
period of the magnetic cycle of some pulsars.
