Sum rule for the linear density response of a driven electronic system

Abstract

Using the covariance of the time-dependent Schrödinger equation under transformation to an accelerated frame of reference, it is shown that the linear density-density response function χ( r, r′; ω) of an electronic system driven by a time-dependent potential at a frequency ω in the presence of a static potential V 0( r) satisfies the sum rule ∫ X( r, r′; ω)[∇ V 0( r′)− mω 2 r′]d r′ = ∇ n 0( r), where n 0( r) is the equilibrium density. The implications of this identity for approximate time-dependent mean field theories are presented.