  The Callan-Harvey mechanism in 2+1 D Jackiw-Rebbi model is revisited. We
analyzed Callan-Harvey anomaly inflow in the massive Chern insulator (quantum
anomalous Hall system) subject to external electric field. In addition to the
conventional current flowing from the bulk to edge due to parity anomaly, we
considered the dissipation of the edge charge due to interaction with external
bosonic bath in 2+1 D and due to external bath of photons in 3+1 D. In the case
of 2+1 D bosonic bath, we found the new stationary state, which is defined by
the balance between Callan-Harvey current and the outgoing flow caused by the
dissipation processes. In the case of 3+1 D photon bath, we found a critical
electric field, below which this balance state can be achieved, but above which
there is no such a balance. Furthermore, we estimated the photon-mediated
transition rate between 2+1 D bulk and 1+1 D topological edge state of the
order of one ns$^{-1}$ (nanosecond) at the room temperature.
