Related papers: N-representability and stationarity in time-depend…

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…

We formulate a time-dependent density functional theory for the coupled dynamics of electrons and nuclei that goes beyond the Born-Oppenheimer (BO) approximation. We prove that the time-dependent marginal nuclear probability density…

The relativistic phase-space representation by means of the usual position and momentum operators for a class of observables with Weyl symbols independent of charge variable (i.e. with any combination of position and momentum) is proposed.…

According to a recent paper by G. Vignale [Phys. Rev. A 77, 062511 (2008), arXiv:0803.2727], the problems arising in the original derivation of time-dependent density functional theory (TDDFT) based on the Runge-Gross (RG) action-integral…

An explicit expression for the quadratic density-response function of a many-electron system is obtained in the framework of the time-dependent density-functional theory, in terms of the linear and quadratic density-response functions of…

The literature on time series of functional data has focused on processes of which the probabilistic law is either constant over time or constant up to its second-order structure. Especially for long stretches of data it is desirable to be…

Noether's calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the…

The time-dependent density functional (TDDFT) equations may be written either for the Kohn-Sham orbitals in Hilbert space or for the single electron density matrix in Liouville space. A collective-oscillator, quasiparticle, representation…

In the well-known Kohn-Sham theory in Density Functional Theory, a fictitious non-interacting system is introduced that has the same particle density as a system of $N$ electrons subjected to mutual Coulomb repulsion and an external…

Using the Runge-Gross theorem that establishes the foundation of Time-dependent Density Functional Theory (TDDFT) we prove that for a given electronic Hamiltonian, choice of initial state, and choice of fragmentation, there is a unique…

Due to the strongly nonlocal nature of $f_{xc}({\bf r},{\bf r}',\omega)$ the {\em scalar} exchange and correlation (xc) kernel of the time-dependent density-functional theory (TDDFT), the formula for Q the friction coefficient of an…

I show that the so-called causality paradox of time-dependent density functional theory arises from an incorrect formulation of the variational principle for the time evolution of the density. The correct formulation not only resolves the…

In this paper, we generalize a previous relativistic $1+1$-dimensional model for two mass-less Dirac particles with relativistic contact interactions to the $N$-particle case. Our model is based on the notion of a multi-time wave function…

We show that the time dependent single electron, nuclear density matrix of an interacting electronic system coupled to nuclear degrees of freedom can be exactly reproduced by that of an electronic system with arbitrarily specified…

In a paper recently published in Phys. Rev. A [arXiv:1010.4223], Schirmer has criticized an earlier work of mine [arXiv:0803.2727], as well as the foundations of time-dependent density functional theory. In Ref.[2], I showed that the…

We present a rigorous formulation of the time-dependent density functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic…

Analytical representations in the time and frequency domains are derived for the most frequently used phenomenological fit functions for non-Debye relaxation processes. In the time domain the relaxation functions corresponding to the…

The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn theorem is found void in general, while many insights into the topological structure of…

We study the mapping between time-dependent densities and potentials for noninteracting electronic systems on lattices. As discovered recently by Baer [J. Chem. Phys. 128, 044103 (2008)], there exist well-behaved time-dependent density…

Inspired by earlier work on the band-gap problem in insulators, we reexamine the treatment of strongly correlated Hubbard-type models within density-functional theory. In contrast to previous studies, the density is fully parametrized by…