Related papers: Domains of time-dependent density-potential mappin…
A probability density function (PDF) of a spatially dependent field provides a means of calculating moments of the field or, equivalently, the proportion of a spatial domain that is mapped to a given set of values. This paper describes a…
The problem of classical particle in linear potential is studied by using the formalism of Hilbert space and tomographic probability distribution. The Liouville equation for this problem is solved by finding the density matrix satisfying…
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…
This paper is concerned with dependence of discrete Sturm-Liouville eigenvalues on problems. Topologies and geometric structures on various spaces of such problems are firstly introduced. Then, relationships between the analytic and…
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…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…
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…
We introduce a new class of Sturm-Liouville operators with periodically modulated parameters. Their spectral properties depend on the monodromy matrix of the underlying periodic problem computed for the spectral parameter equal to $0$.…
Linear response time-dependent density functional theory is used to study low-lying electronic continuum states of targets that can bind an extra electron. Exact formulas to extract scattering amplitudes from the susceptibility are derived…
In the current density functional theory of linear and nonlinear time-dependent phenomena, the treatment of exchange and correlation beyond the level of the adiabatic local density approximation is shown to lead to the appearance of…
Electron-positron interactions have been utilized in various fields of science. Here we develop time-dependent multi-component density functional theory to study the coupled electron-positron dynamics from first principles. We prove that…
In perturbative string theory, one is generally interested in asymptotic observables, such as the S-matrix in flat spacetime, and boundary correlation functions in anti-de Sitter spacetime. However, there are backgrounds in which such…
A fundamental property of a quantum system driven by an external field is that when the field is turned off the positions of its response frequencies are independent of the time at which the field is turned off. We show that this leads to…
One route to numerically propagating quantum systems is time-dependent density functional theory (TDDFT). The application of TDDFT to a particular system's time evolution is predicated on $V$-representability which we have analyzed in a…
An extended time-dependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM), is solved as a time-independent eigenvalue problem for low-lying $2^+$ states in $^{24}$O to understand the foundation of the rather…
We show that classical density functional theory can be based on the constrained search method [M. Levy, Proc. Natl. Acad. Sci. 76, 6062 (1979)]. From the Gibbs inequality one first derives a variational principle for the grand potential as…
Conceiving a molecule as composed of smaller molecular fragments, or subunits, is one of the pillars of the chemical and physical sciences, and leads to productive methods in quantum chemistry. Using a fragmentation scheme, efficient…
We investigate when Taylor expansions can be used to prove the Runge-Gross Theorem, which is at the foundation of Time-Dependent Density Functional Theory (TDDFT). We start with a general analysis of the conditions for the Runge-Gross…
It has been known for some time that the exchange-correlation potential in time-dependent density functional theory is an intrinsically nonlocal functional of the density as soon as one goes beyond the adiabatic approximation. In this paper…
We introduce the position-dependent probability distribution function (PDF) of the smoothed matter field as a cosmological observable. In comparison to the PDF itself, the spatial variation of the position-dependent PDF is simpler to model…