  The local Larmor clock is used to derive a hierarchy of local densities of
states. At the bottom of this hierarchy are the partial density of states for
which represent the contribution to the local density of states if both the
incident and outgoing scattering channel are prescribed. On the next higher
level is the injectivity which represents the contribution to the local density
of states if only the incident channel is prescribed regardless of the final
scattering channel. The injectivity is related by reciprocity to the emissivity
of a point into a quantum channel. The sum of all partial density of states or
the sum of all injectivities or the sum of all emissivities is equal to the
local density of states. The use of the partial density of states is
illustrated for a number of different electron transport problems in mesoscopic
physics: The transmission from a tunneling tip into a mesoscopic conductor, the
discussion of inelastic or phase breaking scattering with a voltage probe, and
the ac-conductance of mesoscopic conductors. The transition from a capacitive
response (positive time-delay) to an inductive response (negative time-delay)
for a quantum point contact is used to illustrate the difficulty in associating
time-scales with a linear response analysis. A brief discussion of the
off-diagonal elements of a partial density of states matrix is presented. The
off-diagonal elements permit to investigate carrier fluctuations away from the
average carrier density. The work concludes with a discussion of the relation
between the partial density of states matrix and the Wigner-Smith delay time
matrix.
