相关论文: Numerical simulations of strong-field processes in…

We present the time-dependent complete-active-space self-consistent-field (TD-CASSCF) method to simulate multielectron dynamics in ultrafast intense laser fields from the first principles. While based on multiconfiguration expansion, it…

The linear Schr\"odinger equation with piecewise constant potential in one spatial dimension is a well-studied textbook problem. It is one of only a few solvable models in quantum mechanics and shares many qualitative features with…

A strategy is developed for writing the time-dependent Schr\"{o}dinger Equation (TDSE), and more generally the Dyson Series, as a convolution equation using recursive Fourier transforms, thereby decoupling the second-order integral from the…

Two examples of recent progress in applications of the Dyson-Schwinger equation (DSE) formalism are presented: (1) Strong coupling quantum electrodynamics in 4 dimensions (QED$_4$) is an often studied model, which is of interest both in its…

A class of non-local non-linear Schrodinger equations(NLSE) is considered in an external potential with space-time modulated coefficient of the nonlinear interaction term as well as confining and/or loss-gain terms. This is a generalization…

We extend our finite difference time domain method for numerical solution of the Schrodinger equation to cases where eigenfunctions are complex-valued. Illustrative numerical results for an electron in two dimensions, subject to a confining…

We have shown that it is possible to model accurately optical phenomena in intense laser fields by taking into account the intensity distribution over the laser beam. We developed a theoretical model that divided an intense laser beam into…

We present an exact single-electron picture that describes the correlated electron dynamics in strong laser fields. Our approach is based on the factorization of the electronic wavefunction as a product of a marginal and a conditional…

With the advent of ultra-high power lasers the nonlinear nature of the vacuum of quantum electrodynamics (QED) can be probed. Due to the highly nonlinear structure of the underlying equations new numerical algorithms are required. A…

A method is proposed for extracting ionization amplitudes from the solution of the time-dependent Schr\"odinger equation (TDSE) describing a system in a time-dependent external field. The method is a hybrid of two earlier developed methods,…

We derive a new time-dependent Schr\"odinger equation(TDSE) for quantum models with non-hermitian Hamiltonian. Within our theory, the TDSE is symmetric in the two Hilbert spaces spanned by the left and the right eigenstates, respectively.…

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary…

We study the suppression of reflections in the numerical simulation of the time-dependent Schr\"odinger equation for strong-field problems on a grid using exterior complex scaling (ECS) as absorbing boundary condition. It is shown that the…

We present analytical results and numerical simulations for a class of nonlinear dispersive equations in two spatial dimensions. These equations are of (derivative) nonlinear Schr\"odinger type and have recently been obtained in \cite{DLS}…

Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…

The classical approximation may be applied to a number of problems in non-equilibrium field theory. The principles and limits of classical real-time lattice simulations are presented, with particular emphasis on the definition of particle…

The state of art of time domain integral equation (TDIE) solvers has grown by leaps and bounds over the past decade. During this time, advances have been made in (i) the development of accelerators that can be retrofitted with these solvers…

The study of strongly out-of-equilibrium states and their time evolution towards thermalization is critical to the understanding of an ever widening range of physical processes. We present a numerical method that for the first time allows…

In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the time-dependent Schr\"odinger equation (TDSE). In our main result, we prove that any pair…

We show that the time-dependent Schr\"odinger equation (TDSE) is the phenomenological dynamical law of evolution unraveled in the classical limit from a timeless formulation in terms of probability amplitudes conditioned by the values of…