PARTIAL DENSITIES OF STATES, SCATTERING MATRICES, AND GREENS-FUNCTIONS

The response of an arbitrary scattering problem to quasistatic perturb ations in the scattering potential is naturally expressed in terms of a set of local partial densities of states and a set of sensitivities each associated with one element of the scattering matrix. We define t he local partial densities of states and the sensitivities in terms of functional derivatives of the scattering matrix and discuss their rel ation to the Green's function. Certain combinations of the local parti al densities of states represent the injectivity of a scattering chann el into the system and the emissivity into a scattering channel. It is shown that the injectivities and emissivities are simply related to t he absolute square of the scattering wave function. We discuss also th e connection of the partial densities of states and the sensitivities to characteristic times. We apply these concepts to a delta barrier an d to the local Larmor clock.