Related papers: Exponential Integrators in Time-Dependent Density …
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…
Based on the work of Gorling and that of Levy and Nagy, density-functional formalism for many Fermionic excited-states is explored through a careful and rigorous analysis of the excited-state density to external potential mapping. It is…
The solution of inverse problems in a variational setting finds best estimates of the model parameters by minimizing a cost function that penalizes the mismatch between model outputs and observations. The gradients required by the numerical…
We consider the numerical approximation of a general second order semi--linear parabolic partial differential equation. Equations of this type arise in many contexts, such as transport in porous media which is fundamental in many…
We use separation of variables as a tool to identify and to analyze exactly soluble time-dependent quantum mechanical potentials. By considering the most general possible time-dependent re-definition of the spatial coordinate, as well as…
We present accurate optical spectra of semiconductors and insulators within a pure Kohn-Sham time-dependent density-functional approach. In particular, we show that the onset of the absorption is well reproduced when comparing to…
We present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency dependent Sternheimer equation,…
Efficiency of time-evolution of quantum observables, and thermal states of quenched hamiltonians, is studied using time-dependent density matrix renormalization group method in a family of generic quantum spin chains which undergo a…
A new class of methods is introduced for solving the Kohn-Sham equations of density functional theory, based on constructing a mapping dynamically between the Kohn-Sham system and an auxiliary system. The resulting auxiliary density…
We introduce a non-equilibrium density-functional theory of local temperature and associated local energy density that is suited for the study of thermoelectric phenomena. The theory rests on a local temperature field coupled to the…
Simulation of geothermal systems is challenging due to coupled physical processes in highly heterogeneous media. Combining the exponential Rosenbrock--Euler and Rosenbrock-type methods with control-volume (two-point flux approximation)…
The exponential fitting technique uses information on the expected behaviour of the solution of a differential problem to define accurate and efficient numerical methods. In particular, exponentially fitted methods are very effective when…
For trigonometric and modified trigonometric integrators applied to oscillatory Hamiltonian differential equations with one or several constant high frequencies, near-conservation of the total and oscillatory energies are shown over time…
The integrable time-dependent central potentials that admit linear and quadratic first integrals other than those constructed from the angular momentum are determined. It is shown explicitly that previous answers to this problem are…
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…
We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of…
To integrate large systems of nonlinear differential equations in time, we consider a variant of nonlinear waveform relaxation (also known as dynamic iteration or Picard-Lindel\"of iteration), where at each iteration a linear inhomogeneous…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
A quantitative definition of numerical stiffness for initial value problems is proposed. Exponential integrators can effectively integrate linearly stiff systems, but they become expensive when the linear coefficient is a matrix, especially…
The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation. Here, we study an alternative…