Related papers: Numerical simulations of strong-field processes in…
We introduce a numerical strategy to efficiently solve the out-of-equilibrium Dyson equation in the transient regime. By discretizing the equation into a compact matrix form and applying state-of-the-art matrix compression techniques, we…
We study a nonlinear Schr\"odinger equation which arises as an effective single particle model in X-ray Free Electron Lasers (XFEL). This equation appears as a first-principles model for the beam-matter interactions that would take place in…
Schr\"odinger equations with time-dependent potentials are of central importance in quantum physics and theoretical chemistry, where they aid in the simulation and design of systems and processes at atomic scales. Numerical approximation of…
The semiclassical Schr\"odinger equation with time-dependent potentials is an important model to study electron dynamics under external controls in the mean-field picture. In this paper, we propose two multiscale finite element methods to…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
Particle-in-cell codes are now standard tools for studying ultra-intense laser-plasma interactions. Motivated by direct laser acceleration of electrons in sub-critical plasmas, we examine temporal resolution requirements that must be…
The creation of the new particles by the interaction of the ultrarelativistic ions,from Large Hadron Collider(LHC), and attosecond laser pulse open new possibilities for laser physicists community .In this paper we propose the hyperbolic…
The Landau-Lifshitz equation provides an efficient way to account for the effects of radiation reaction without acquiring the non-physical solutions typical for the Lorentz-Abraham-Dirac equation. We solve the Landau-Lifshitz equation in…
The formulation of the time-dependent Schrodinger equation in terms of coupled-cluster theory is outlined, with emphasis on the bivariational framework and its classical Hamiltonian structure. An indefinite inner product is introduced,…
Nondipole effects in the atomic dynamic interference are investigated by numerically solving the time-dependent Schr\"odinger equation~(TDSE) of hydrogen. It is found that the inclusion of nondipole corrections in the TDSE can induce…
Theoretical treatments of strong-field physics have long relied on the numerical solution of the time-dependent Schr\"odinger equation. The most effective such treatments utilize a discrete spatial representation---a grid. Since most…
Heavy-ion collision is an important tool to understand the dense nuclear matter properties. In order to understand the results of the heavy-ion collision experiments, both theoretical approaches to dense nuclear matter using effective…
For electromagnetic transient (EMT) simulation of a power system, a state-space-based approach needs to solve state-space EMT equations by using numerical integration methods, e.g., the Euler method, Runge-Kutta methods, and…
Solving the time-dependent quantum many-body Schr\"odinger equation is a challenging task, especially for states at a finite temperature, where the environment affects the dynamics. Most existing approximating methods are designed to…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
We report on 3D-3V particle-in-cell simulations of fast-ion energy-loss rates in cold, weakly-magnetized, weakly-coupled plasma where the electron gyroradius, $\rho_{e}$, is comparable to or less than the Debye length, $\lambda_{De}$, and…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Numerical simulation of atmospheric turbulence is one of the biggest bottlenecks in developing computational techniques for solving the inverse problem in long-range imaging. The classical split-step method is based upon numerical wave…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
To address the magnetization dynamics in ferromagnetic materials described by the Landau-Lifshitz-Gilbert equation under large damping parameters, a third-order accurate numerical scheme is developed by building upon a second-order method…