Dresden 2009 – wissenschaftliches Programm

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O: Fachverband Oberflächenphysik

O 49: Ab-initio approaches to excitations in condensed matter II

O 49.4: Vortrag

Donnerstag, 26. März 2009, 11:15–11:30, SCH 251

Kohn-Sham scheme for frequency dependent linear response — •Ryan Requist and Oleg Pankratov — Lehrstuhl für Theoretische Festkörperphysik, Universität Erlangen-Nürnberg

Due to the so-called causality paradox, the Kohn-Sham scheme in time dependent density functional theory cannot be derived from a stationary principle of the form δ A/δ n = 0, where A[n] is the density functional for the quantum mechanical action. As Vignale has recently shown [1], the density-functional formulation of the action principle contains boundary terms. Therefore, the exact exchange-correlation potential cannot be calculated from the functional derivative of a universal functional. However, we find that the second-order quasienergy, K_v⁽²⁾, satisfies a stationary principle δ K_v⁽²⁾/δ n_ω⁽¹⁾=0, where n_ω⁽¹⁾ is the linear response density induced by a harmonic perturbation with frequency ω. This is not inconsistent with Vignale’s result because boundary terms vanish in this case. The stationary principle can serve as a basis for the linear response Kohn-Sham scheme. The first-order exchange-correlation potential v_xc⁽¹⁾ is the functional derivative of the exchange-correlation part of K_v⁽²⁾. With the same approach, we also find a stationary principle and linear response Kohn-Sham scheme in the time dependent extension of reduced density matrix functional theory, in which the basic variable is the one-body reduced density matrix.

[1] G. Vignale, Phys. Rev. A, 77, 062511 (2008).