Related papers: On the density-potential mapping in time-dependent…
This work studies in detail the possibility of defining a one-to-one mapping from charge densities as obtained by the time-dependent Schr\"odinger equation to external potentials. Such a mapping is provided by the Runge-Gross theorem and…
The key element in time-dependent density functional theory is the one-to-one correspondence between the one-particle density and the external potential. In most approaches this mapping is transformed into a certain type of Sturm-Liouville…
The mapping of time-dependent densities on potentials in quantum mechanics is critically examined. The issue is of significance ever since Runge and Gross (Phys. Rev. Lett. 52, 997 (1984)) established the uniqueness of the mapping, forming…
In this work we review the mapping from densities to potentials in quantum mechanics, which is the basic building block of time-dependent density-functional theory and the Kohn-Sham construction. We first present detailed conditions such…
The electron density $n(\rb,t)$, which is the central tool of time-dependent density functional theory, is presently considered to be derivable from a one-body time-dependent potential $V(\rb,t)$, via one-electron wave functions satisfying…
In this work, the existence, uniqueness and regularity of solutions to the time-dependent Kohn-Sham equations are investigated. The Kohn-Sham equations are a system of nonlinear coupled Schr\"odinger equations that describe multi-particle…
When can we map a classical density profile to an external potential? In equilibrium, without time dependence, the one-body density is known to specify the external potential that is applied to the many-body system. This mapping from a…
We use analytic (current) density-potential maps of time-dependent (current) density functional theory (TD(C)DFT) to inverse engineer analytically solvable time-dependent quantum problems. In this approach the driving potential (the control…
The formalism of density functional theory (DFT) can be easily extended to the time dependent case (TDDFT). However, while in the static case the theory is well established and is expected to be, at least in principle, an exact approach for…
Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we…
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…
In this work we investigate the functional differentiability of the time-dependent many-body wave function and of derived quantities with respect to time-dependent potentials. For properly chosen Banach spaces of potentials and wave…
By minimizing the difference between the left- and the right-hand sides of the many-body time-dependent Schr\"{o}dinger equation with the Slater-determinant wave-function, we derive a non-adiabatic and self-interaction free time-dependent…
A rigorous formulation of time-dependent current density functional theory (TDCDFT) on a lattice is presented. The density-to-potential mapping and the ${\cal V}$-representability problems are reduced to a solution of a certain nonlinear…
We investigate the existence and properties of effective potentials in time-dependent density functional theory. We outline conditions for a general solution of the corresponding Sturm-Liouville boundary value problems. We define the set of…
Time-Dependent Density Functional Theory is mathematically formulated through non-linear coupled time-dependent 3-dimensional partial differential equations and it is natural to expect a strong sensitivity of its solutions to variations of…
The linear Schr\"odinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum mechanics and shares many qualitative features with…
A time-dependent density functional theory (TDDFT) for a quantum many-body system on a lattice is formulated rigorously. We prove the uniqueness of the density-to-potential mapping and demonstrate that a given density is $v$-representable…
Time-dependent density functionals in principle depend on the initial state of the system, but this is ignored in functional approximations presently in use. For one electron it is shown there is no initial-state dependence: for any…
The response of an extended periodic system to a homogeneous field (of wave-vector $q=0$) cannot be obtained from a $q=0$ time-dependent density functional theory (TDDFT) calculation, because the Runge-Gross theorem does not apply.…