  Over the past decade, there has been a great interest in topological effects,
with concepts originally developed in the context of electron transport in
condensed matter platforms now being extended to optical systems. While
topological properties in electronic systems are often linked to the
quantization of electric conductivity observed in the integer quantum Hall
effect, a direct analogue in optics remains elusive. In this study, we bridge
this gap by demonstrating that the response of the Poynting vector (which may
be regarded as a "photon current") to the mechanical acceleration of a medium
provides a precise photonic analogue of the electric conductivity. In
particular, it is shown that the photonic conductivity determines the energy
irreversibly transferred from a periodic mechanical driving of the medium to
the electromagnetic field. Furthermore, it is demonstrated that for
nonreciprocal systems enclosed in a cavity, the constant acceleration of the
system induces a flow of photons along a direction perpendicular to the
acceleration, analogous to the Hall effect but for light. The spectral density
of the photonic conductivity is quantized in the band gaps of the bulk region
with the conductivity quantum determined by the gap Chern number.
