SUM-RULE FOR THE LINEAR DENSITY RESPONSE OF A DRIVEN ELECTRONIC SYSTEM

Using the covariance of the time-dependent Schrodinger equation under transformation to an accelerated frame of reference, it is shown that the linear density-density response function (chi)(r, r'; omega) of an electronic system driven by a time-dependent potential at a frequency omega in the presence of a static potential V-o(r) satisfies the sum rule integral (chi)(r, r'; omega) [del Vo(r')- m omega(2)r'] dr' - del n(o)(r), where n(o)(r) is the equilibrium density, The implications of this identity for approximate time-dependent mean field theories are presented.