Related papers: An Efficient and Accurate Grid Method for Solving …

Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…

We discuss a method of solving the time dependent Schrodinger equation for atoms with two active electrons in a strong laser field, which we used in a previous paper [A. Scrinzi and B. Piraux, Phys. Rev. A 56, R13 (1997)] to calculate…

Simulation of 3D low-frequency electromagnetic fields propagating in the Earth is computationally expensive. We present a fictitious wave domain high-order finite-difference time-domain (FDTD) modelling method on nonuniform grids to compute…

The accurate description of the non-linear response of many-electron systems to strong-laser fields remains a major challenge. Methods that bypass the unfavorable exponential scaling with particle number are required to address larger…

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…

We present a simple method to solve spherical harmonics moment systems, such as the the time-dependent $P_N$ and $SP_N$ equations, of radiative transfer. The method, which works for arbitrary moment order $N$, makes use of the specific…

The Korteweg-de Vries (KdV) equation is a fundamental partial differential equation that models wave propagation in shallow water and other dispersive media. Accurately solving the KdV equation is essential for understanding wave dynamics…

A fast and stable method is formulated to compute the time evolution of a wavefunction by numerically solving the time-dependent Schr{\"o}dinger equation. This method is a real space/real time evolution method implemented by several…

We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time-adaptive Dirichlet-Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler…

The Variational Theory of Complex Rays (VTCR) is an indirect Trefftz method designed to study systems governed by Helmholtz-like equations. It uses wave functions to represent the solution inside elements, which reduces the dispersion error…

We present angular distributions of photoelectrons of atomic model systems excited by intense linearly polarized laser pulses in the VUV- and XUV-regime. We solve the multi-dimensional time-dependent Schr\"odinger equation for one particle…

The extended KdV equation is a nonlinear dispersive wave model that is asymptotically or variationally derived from the full dispersive Euler shallow water waves equations when gravity-capillary and higher order nonlinear effects are taken…

This paper presents a self-contained factorization for the delay Vandermonde matrix (DVM), which is the super class of the discrete Fourier transform, using sparse and companion matrices. An efficient DVM algorithm is proposed to reduce the…

A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…

A general {\it ab-initio} and non-perturbative method to solve the time-dependent Schr\"odinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom, i.e., beyond the models of quasi-one-electron or…

We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as…

Solving the time-dependent Schr\"odinger equation is an important application area for quantum algorithms. We consider Schr\"odinger's equation in the semi-classical regime. Here the solutions exhibit strong multiple-scale behavior due to a…

We study the recently-proposed hyperbolic approximation of the Korteweg-de Vries equation (KdV). We show that this approximation, which we call KdVH, possesses a rich variety of solutions, including solitary wave solutions that approximate…

An approximate method for solving the rate equations for the hydrogen populations was extended and implemented in the three-dimensional radiation (magneto-)hydrodynamics code CO5BOLD. The method is based on a model atom with six energy…

We investigate the dynamical phase evolution of Coulomb-focused electrons in strong-field ionization. We diffract the electrons with an ultrashort standing light wave to track their time-dependent phase. Our findings show that low-energy…