Related papers: On the density-potential mapping in time-dependent…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
Inspired by the formulation of quantum-electrodynamical time-dependent density functional theory (QED-TDDFT) by Rubio and coworkers, we propose an implementation that uses dimensionless amplitudes for describing the photonic contributions…
The Kohn-Sham approach to time-dependent density-functional theory (TDDFT) can be formulated, in principle exactly, by invoking the force-balance equation for the density, which leads to an explicit expression for the exchange-correlation…
We show that the time-dependent particle density $n(\vec r,t)$ and the current density ${\vec j}(\vec r,t)$ of a many-particle system that evolves under the action of external scalar and vector potentials $V(\vec r,t)$ and $\vec A(\vec…
We present an extension of the density-functional theory (DFT) formalism for lattice gases to systems with internal degrees of freedom. In order to test approximations commonly used in DFT approaches, we investigate the statics and dynamics…
Analytic solutions to the time-dependent Schr\"odinger equation for cutoff wave initial conditions are used to investigate the time evolution of the transmitted probability density for tunneling. For a broad range of values of the potential…
We explore whether quantum field theory can be understood as the statistical mechanics of a time-reversal-invariant stochastic generalization of Hamiltonian dynamics. The motivation for this project, started with this paper, is to assign…
We consider time-dependent Schroedinger equations in one dimension with double well potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest…
We present a numerical study of a derivative nonlinear Schr\"odinger equation with a general power nonlinearity, $|\psi|^{2\sigma}\psi_x$. In the $L^2$-supercritical regime, $\sigma>1$, our simulations indicate that there is a finite time…
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…
This paper gives an introduction to the Keldysh formalism, with emphasis on its usefulness in time-dependent density functional theory. In the first part we introduce the Keldysh contour and the one-particle Green function defined on this…
We consider d-dimensional time dependent Schr\"odinger equations on the Hilbert space of square integrable functions. We assume magnetic and scalar potentials are almost critically singular with respect to spatial variables both locally and…
We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the…
We calculate the exact Kohn-Sham potential that describes, within time-dependent density-functional theory, the propagation of an electron quasiparticle wavepacket of non-zero crystal momentum added to a ground-state model semiconductor.…
The Schr\"odinger equation in high dimensions describes the evolution of a quantum system. Assume that we are given the evolution map sending each initial state $f\in L^2(\mathbb{R}^n)$ of the system to the corresponding final state at a…
We prove existence of propagators for a time dependent Schr\"odinger equation with a new class of softened Coulomb potentials, which we allow to be time dependent, in the context of time dependent density functional theory. We compute…
A new class of time-energy uncertainty relations is directly derived from the Schr\"odinger equations for time-dependent Hamiltonians. Only the initial states and the Hamiltonians, but neither the instantaneous eigenstates nor the full…
We study the collective dynamics of colloidal suspensions in the presence of a time-dependent potential, by means of dynamical density functional theory. We consider a non-linear diffusion equation for the density and show that spatial…
We employ the density matrix renormalization group to construct the exact time-dependent exchange correlation potential for an impurity model with an applied transport voltage. Even for short-ranged interaction we find an infinitely…
It is shown here that Kohn-Sham equations cannot be derived from Hohenberg-Kohn theory without an additional postulate. Assuming that a functional derivative with respect to total electron density exists leads in general to a theory…