相关论文: Existence and uniqueness of solutions to the time-…

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…

In this paper, a new analysis for existence, uniqueness, and regularity of solutions to a time-dependent Kohn-Sham equation is presented. The Kohn-Sham equation is a nonlinear integral Schroedinger equation that is of great importance in…

We study the question of existence and uniqueness for the finite temperature Kohn-Sham equations. For finite volumes, a unique soluion is shown to exists if the effective potential satisfies a set of general conditions and the coupling…

Predictivity of the Kohn-Sham approach to dynamical problems, when regarded as an initial value problem in a time-dependent density functional framework, is analysed for a class of models for which the argument devised in the work of Maitra…

The frequency-dependent exchange-correlation potential, which appears in the usual Kohn-Sham formulation of a time-dependent linear response problem, is a strongly nonlocal functional of the density, so that a consistent local density…

We prove that to each initial datum in a set of positive measure in phase space, there exist uncountably-many associated weak solutions of Newton's equations of motion which govern the dynamics of two non-spherical sets with real-analytic…

This paper is concerned with an initial-boundary value problem of the two-dimensional inhomogeneous primitive equations with density-dependent viscosity. The global well-posedness of strong solutions is established, provided the initial…

Time dependent quantum systems are the subject of intense inquiry, in mathematics, science, and engineering, particularly at the atomic and molecular levels. In 1984, Runge and Gross introduced time dependent density functional theory…

Basic issues of the time-dependent density-functional theory are discussed, especially on the real-time calculation of the linear response functions. Some remarks on the derivation of the time-dependent Kohn-Sham equations and on the…

The inclusion of nucleonic exchange energy has been a long-standing challenge for the relativistic density functional theory (RDFT) in nuclear physics. We propose an orbital-dependent relativistic Kohn-Sham density functional theory to…

A numerical scheme for solving the time-evolution of wave functions under the time dependent Kohn-Sham equation has been developed. Since the effective Hamiltonian depends on the wave functions, the wave functions and the effective…

We consider a stochastic differential equation in a Hilbert space with time-dependent coefficients for which no general existence and uniqueness results are known. We prove, under suitable assumptions, existence and uniqueness of a measure…

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…

Nuclear implementation of the density functional theory (DFT) is at present the only microscopic framework applicable to the whole nuclear landscape. The extension of DFT to superfluid systems in the spirit of the Kohn-Sham approach, the…

In this paper, we prove the existence and uniqueness of the solution for neutral stochastic differential delay equations with locally monotone coefficients by using numerical approximation. An example is provided to illustrate our theory.

The Hohenberg-Kohn theorem and the Kohn-Sham equations, which are at the basis of the Density Functional Theory, are reformulated in terms of a particular many-body density, which is translational invariant and therefore is relevant for…

By inverting the time-dependent Kohn-Sham equation for a numerically exact dynamics of the helium atom, we show that the dynamical step and peak features of the exact correlation potential found previously in one-dimensional models persist…

In this paper we are concerned with the stochastic partial differential equations of super-fast diffusion processes describing behavior of plasma dX(t)-{\Delta}ln(X(t)+1)dt=\surd(Q)dW(t), in (0,T)\timesO, where O is a bounded open subset of…

We generalize to the time-dependent case the stationary Internal DFT / Kohn-Sham formalism presented in Ref. [14]. We prove that, in the time-dependent case, the internal properties of a self-bound system (as an atomic nuclei) are all…

A generalization of the Kohn--Sham approach is derived where the correlation-energy functional depends on the one-particle density matrix of noninteracting states and on the external potential from the interacting target-state. The…