A unified approach to the density-potential mapping in a family of time-dependent density functional theories

It is shown that the density-potential mapping and the ${\cal V}$-representability problems in the time-dependent current density functional theory (TDCDFT) are reduced to the solution of a certain many-body nonlinear Schr\"odinger equation (NLSE). The derived NLSE for TDCDFT adds a link which bridges the earlier NLSE-based formulations of the time-dependent deformation functional theory (TDDefFT) and the time-dependent density functional theory (TDDFT). We establish close relations between the nonlinear many-body problems which control the existence of TDCDFT, TDDFT, and TDDefFT, and thus develop a unified point of view on the whole family of the TDDFT-like theories.Comment: RevTeX4, 15 page

Time-dependent current density functional theory via time-dependent deformation functional theory: A constrained search formulation in the time domain

The logical structure and the basic theorems of time-dependent current density functional theory (TDCDFT) are analyzed and reconsidered from the point of view of recently proposed time-dependent deformation functional theory (TDDefFT). It is shown that the formalism of TDDefFT allows to avoid a traditional external potential-to-density/current mapping. Instead the theory is formulated in a form similar to the constrained search procedure in the ground state DFT. Within this formulation of TDCDFT all basic functionals appear from the solution of a constrained universal many-body problem in a comoving reference frame, which is equivalent to finding a conditional extremum of a certain universal action functional. As a result the physical origin of the universal functionals entering the theory, as well as their proper causal structure becomes obvious. In particular, this leaves no room for any doubt concerning predictive power of the theory.Comment: revtex4, 24 page

Orbital momentum Hall effect in p-doped graphane

It is shown that an electric field applied to p-doped graphane generates a dissipationless orbital momentum Hall current. In the clean limit the corresponding Hall conductivity is independent of the concentration of holes. The Hall effect is related to the $2\pi$-Berry phase accumulated when heavy and light holes are transported around the degeneracy point in the center of the Brillouin zone. This also leads to the orbital momentum edge currents in the equilibrium state, and to the accumulation of the orbital momentum at the edges when the system is driven out of equilibrium.Comment: RevTeX 4, 4 pages, 2 figures, final versio