TIME DEPENDENT DENSITY FUNCTIONAL THEORY ... - TDDFT.org

Time-dependent exchange-correlation current
density functionals with memory
Yair Kurzweil and Roi Baer
Department of Physical Chemistry and the Lise Meitner Minerva-Center for Computational
Quantum Chemistry, the Hebrew University of Jerusalem, Jerusalem 91904 Israel.
Most present applications of time-dependent density functional theory use adiaba tic functionals,
i.e. the effective potential at time t is determined solely by the density at the same time. Our work
discusses a method that aims to go beyond this approximation, by incorporating ”memory” effects:
the potential will depend also on the history. We add to the adiabatic approximation an additional
part that includes memory and yields a functional that is totally consistent with known dynamical
properties of the homogeneous electron gas (in the linear response limit). In order to achieve this,
we write down an action principle from which Kohn-Sham equations are derived for description of
the time-dependent electron density and fluid velocity field. We construct the action on Lagrangian
coordinate s system and pseudo time domain (Keldysh contour). Therefore, action principle is built
in such a way that it is Galilean invariant and yields causal equations.
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