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

R. F. Bishop

R. F. Bishop

Anna Minguzzi

We extend a sum rule, resulting from the covariance properties of the Schroedinger equation under transformation in an accelerated frame and originally derived for an inhomogeneous electron system, to the linear-density response functions of a confined Bose-condensed gas at finite temperature. We apply the sum rule to test some approximate theories and to show that in the case of a harmonic confinement the random-phase approximation includes the Kohn modes in its spectrum.

Barry Bradlyn, Peter M. Abbamonte

Sum rules for response functions represent some of the few exact results in many-body physics, relating the dynamical response functions to equilibrium ground state properties. To date, however, sum rules have been examined primarily for linear response functions. In this work, the authors introduce a spectral density representation for second-order response functions, using it to systematically derive families of sum rules, including a nonlinear extension of the well-known $f$-sum rule. This work places important constraints on future nonlinear spectroscopic experiments.

Arnold J. Glick