  To apply the scattering approach for the problem of AC transport through
coherent quantum conductors, various partial density of states must be
evaluated. If the global partial density of states (GPDOS) is calculated
externally using the energy derivatives of the scattering matrix, the results
are not precise unless the conductor has a large scattering volume. We propose
a local formula for GPDOS which is suitable for any finite scattering volume.
We apply this formula to compute the emittance of a two-dimensional quantum
wire under the multi-mode and finite temperature condition.
