Time-dependent exchange-correlation current density functionals with memory

Most present applications of time-dependent density functional theory use adiabatic functionals, i.e. the effective potential at time t is determined solely by the density at the same time. This paper 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 consis-tent 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. The action principle is built in such a way that it is Galilean invariant and yields causal equations.