Partial densities of states, scattering matrices, and Green’s functions

Abstract

The response of an arbitrary scattering problem to quasi-static perturbations 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 the local partial densities of states and the sensitivities in terms of functional derivatives of the scattering matrix and discuss their relation to the Green's function. Certain combinations of the local partial densities of states represent the injectivity of a scattering channel into the system and the emissivity into a scattering channel. It is shown that the injectivities and emissivities are simply related to the absolute square of the scattering wave-function. We discuss also the connection of the partial densities of states and the sensitivities to characteristic times. We apply these concepts to a δ-barrier and to the local Larmor clock.

Second-order non-linear conductance of a two-dimensional mesoscopic conductor

“…In comparison, for both 1D and 2D scattering problems involving a δ potential barrier, the sensitivity has been derived analytically in Ref. [13] and [10]. There, η 11 shows strong spatial regular oscillations.…”

“…As discussed in Section 2 η αβ appears naturally in the theoretical formalism, and it essentially describes the local (internal) electric current response of the scattering problem when there is a small local potential change. It is related to the real part of the diagonal elements of the scattering Green's function [13]. From Fig.…”

“…the change of the electrochemical potential at a lead. We are aware of two ways of calculating the sensitivity [13]. The first is to evaluate δs αβ /δU directly by introducing a δ-function of infinitesimal strength δU inside the scattering region.…”

“…is called sensitivity [13] which measures the local electric current response to an external perturbation. u γ (r) is the characteristic potential which measures the variation of the potential landscape of the scattering volume due to the perturbation [1].…”

The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics

“…a set of local density of states states [6,7,8,9,10] which we call partial densities of states which are related to spin precession and in terms of sensitivities which are related to spin rotation. The partial densities of states, below abbreviated as PDOS, are useful to understand a number of transport problems: the transmission probability from a tunneling microscope tip into a multiterminal mesoscopic conductor [10] can be expressed in terms of PDOS, the absorption of carriers by an optical potential (a potential with a small imaginary component), inelastic scattering and dephasing caused by a weak coupling voltage probe, and the low frequency transport in mesoscopic conductors.…”