An alternative form of the variational principle is set up by defining an action functional which takes explicit account of the time path and thus is different from that used traditionally in time-dependent density-functional theory. This has the attractive feature of not having the formal difficulties in defining the effective potential and the effective interaction as its functional derivatives. Also, the Berry phase, not explicitly found at first sight in a time-dependent density-functional theory, is shown to reside in this action functional. It lies buried as the sum over the individual phases of the occupied states associated with the time-dependent Kohn-Sham orbitals. Some recent work on superconductivity and ferroelectricity in the literature are cited as examples of the Berry-phase considerations developed here. \textcopyright{} 1996 The American Physical Society.
The quantum dynamics of a correlated quasi-twodimensional (q2d) electron system showing the Quantum Hall Effect has been investigated. Galilei transformations are discussed for the correct description of quantum mechanical states in crossed electric and magnetic fields. Our quantum liquid site model with quasibosons carrying electromagnetic flux quanta uses a spatio-temporary varying configuration of sites {R(t)}. Due to the nontrivial topology of the system and the multiple degeneracy of its ground state non Abelean Berry phases appear in the adiabatic time evolution. The calculation of the effective action functional has been carried out on the basis of a path integral approach. It is shown that the Berry phases entering the Greens function produce a Chern-Simons-like topological action term. Our theory yields a quantized conductivity tensor and, thus, exibita Quantum Hall behaviour. In calculating the local density of states of the inhomogeneous quantum liquid one obtains a remarkable broadening of peaks and a reduction of their heights.