Related papers: Spectral-based Propagation Schemes for Time-Depend…
An efficient algorithm for time propagation of the time-dependent Kohn-Sham equations is presented. The algorithm is based on dividing the Hamiltonian into small time steps and assuming that it is constant over these steps. This allows for…
We examine the performance of various time propagation schemes using a one-dimensional model of the hydrogen atom. In this model the exact Coulomb potential is replaced by a soft-core interaction. The model has been shown to be a reasonable…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
In this paper, we present a proof-of-concept quantum algorithm for simulating time-dependent Hamiltonian evolution by reducing the problem to simulating a time-independent Hamiltonian in a larger space using a discrete clock Hamiltonian…
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
In this study, we provide a novel wave packet propagation method that generalizes the Hagedorn approach by introducing alternative primitive basis sets that are better suited to describe different physical processes. More precisely, in our…
X-ray absorption spectroscopy (XAS) is a leading technique for understanding structural changes in advanced battery materials such as lithium-excess cathodes. However, extracting critical information like oxidation states from the…
A numerical scheme is proposed for the solution of the three-dimensional radiative transfer equation with variable optical depth. We show that time-dependent ray tracing is an attractive choice for simulations of astrophysical ionization…
We discuss time dependent quantum systems on bounded domains. Our work may be viewed as a framework for several models, including linear iterations involved in time dependent density functional theory (TDDFT), the Hartree-Fock model, or…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
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 present a computationally tractable scheme of time-dependent transport phenomena within open-boundary time-dependent density-functional-theory. Within this approach all the response properties of a system are determined from the…
The numerical solution of time-dependent radiative transfer problems is challenging, both, due to the high dimension as well as the anisotropic structure of the underlying integro-partial differential equation. In this paper we propose a…
We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-art quantum algorithm, i.e., it scales linearly in evolution…
The goal of this presentation is to highlight various computational techniques used to study dynamics of quantum many-body systems. We examine the projection and variable phase methods being applied to multi-channel problems of scattering…
We propose highly accurate finite-difference schemes for simulating wave propagation problems described by linear second-order hyperbolic equations. The schemes are based on the summation by parts (SBP) approach modified for applications…
We use the Gaussian Phase-Space Representation to solve the real-time dynamic of interacting fermions in 1D, 2D, and 3D systems. The method is exact up to a spiking point, which represents a limit on the practical simulation time. The…
Computational modeling of charged species transport has enabled the analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck (PNP)…
Atoms, molecules or excitonic quasiparticles, for which excitations are induced by external radiation fields and energy is dissipated through radiative decay, are examples of driven open quantum systems. We explain the use of…
A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on…