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We reviewed the time-dependent multiconfiguration self-consistent-field (TD-MCSCF) method and the time-dependent optimized coupled-cluster (TD-OCC) method for first-principles simulations of high-field phenomena such as tunneling ionization and high-order harmonic generation in atoms and molecules irradiated by a strong laser field. These methods provide a flexible and systematically improvable description of the multielectron dynamics by expressing the all-electron wavefunction by configuration interaction expansion or coupled-cluster expansion, using time-dependent one-electron orbital functions. The time-dependent variational principle plays a key role in deriving these methods while satisfying gauge invariance and Ehrenfest theorem. The real-time/real-space implementation with an absorbing boundary condition enables the simulation of high-field processes involving multiple excitation and ionization. We present a detailed, comprehensive discussion of such features of the TD-MCSCF and TD-OCC methods. Key words: TD-MCSCF, TD-OCC, high-field phenomena, electron dynamics, 1. Introduction High-field physics (also known as strong field physics) is a field that studies high-field phenomena such as abovethreshold ionization, tunneling ionization, high-order harmonic generation (HHG), and nonsequential double [...]

We present an implementation of the multiconfiguration time-dependent Hartree-Fock method hased on the adaptive finite element method for molecules under intense laser pulses. For efficient simulations, orbital functions are propagated by a stable propagator using the short iterative Arnoldi scheme and our implementation is parallelized for distributed memory computing. This is demonstrated by simulating high-harmonic generation from a water molecule and achieves a simulation of multielectron dynamics with overwhelmingly less computational time, compared to our previous work [Sawada, R. et al. Phys. Rev. A, 2016, 93, 023434]. Key words: Ab initio simulation, multielectron dynamics in molecules, intense laser field, TD-MCSCF method, 1. Introduction Multielectron dynamics studied in strong-field physics and attosecond science is a complicated phenomenon, which includes non-perturbative and nonlinear effects, and multiple states or paths excited by ultrashort pulses. [...]

We present a new filtered low-regularity Fourier integrator for the cubic nonlinear Schrödinger equation based on recent time discretization and filtering techniques. For this new scheme, we perform a rigorous error analysis and establish better convergence rates at low regularity than known for classical schemes in the literature so far. In our error estimates, we combine the better local error properties of the new scheme with a stability analysis based on general discrete Strichartz-type estimates. The latter allow us to handle a much rougher class of solutions as the error analysis can be carried out directly at the level of [Formula omitted] compared to classical results in dimension d, which are limited to higher-order (sufficiently smooth) Sobolev spaces [Formula omitted] with [Formula omitted]. In particular, we are able to establish a global error estimate in [Formula omitted] for [Formula omitted] solutions which is roughly of order [Formula omitted] in dimension [Formula omitted] ( [Formula omitted] denoting the time discretization parameter). This breaks the 'natural order barrier' of [Formula omitted] for [Formula omitted] solutions which holds for classical numerical schemes (even in combination with suitable filter functions)., Author(s): Alexander Ostermann [sup.1] , Frédéric Rousset [sup.2] , Katharina Schratz [sup.3] Author Affiliations: (1) grid.5771.4, 0000 0001 2151 8122, Department of Mathematics, University of Innsbruck, , Technikerstr. 13, 6020, [...]

By using the pseudo-metric introduced in Golse and Paul (Arch Ration Mech Anal 223:57-94, 2017), which is an analogue of the Wasserstein distance of exponent 2 between a quantum density operator and a classical (phase-space) density, we prove that the convergence of time splitting algorithms for the von Neumann equation of quantum dynamics is uniform in the Planck constant [Formula omitted]. We obtain explicit uniform in [Formula omitted] error estimates for the first-order Lie-Trotter, and the second-order Strang splitting methods., Author(s): François Golse [sup.1], Shi Jin [sup.2], Thierry Paul [sup.3] [sup.4] Author Affiliations: (1) grid.10877.39, 0000000121581279, CMLS, École polytechnique, , 91128, Palaiseau Cedex, France (2) grid.16821.3c, 0000 0004 0368 8293, [...]

In this paper, we review recent progress on two related issues. Firstly, the discretisation of partial differential equations of quantum mechanics in a semiclassical regime. Due to the presence of a small parameter, such equations exhibit high oscillations and multiscale behaviour, rendering them difficult to discretise. We describe a methodology, using symmetric Zassenhaus splittings in a free Lie algebra, which allows for their exceedingly fast and accurate numerics. The imperative of preserving the unitarity of the underlying flow takes us to the second theme of this paper, approximation of derivatives by skew-symmetric matrices. Here, we identify a gap in the elementary theory of finite-difference approximations: in the presence of Dirichlet boundary conditions, it is impossible to approximate the derivative to order higher than two on a uniform grid! This motivates the investigation of skew symmetry on non-uniform grids, an endeavour which, although still in its infancy, is already replete with interesting results. We conclude by discussing a number of generalisations and open problems., Author(s): Arieh Iserles[sup.1] Author Affiliations: (1) Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberfoce Rd., CB3 0WA, CambridgeUK Introduction Computational partial differential equations [...]

We rigorously study a novel type of trigonometric Fourier collocation methods for solving multi-frequency oscillatory second-order ordinary differential equations (ODEs) with a principal frequency matrix . If is symmetric and positive semi-definite and for a smooth function , then this is a multi-frequency oscillatory Hamiltonian system with the Hamiltonian where [Formula omitted]. The solution of this system is a nonlinear multi-frequency oscillator. The new trigonometric Fourier collocation method takes advantage of the special structure brought by the linear term [Formula omitted], and its construction incorporates the idea of collocation methods, the variation-of-constants formula and the local Fourier expansion of the system. The properties of the new methods are analysed. The analysis in the paper demonstrates an important feature, namely that the trigonometric Fourier collocation methods can be of an arbitrary order and when , each trigonometric Fourier collocation method creates a particular Runge-Kutta-Nystrom-type Fourier collocation method, which is symplectic under some conditions. This allows us to obtain arbitrary high-order symplectic methods to deal with a special and important class of systems of second-order ODEs in an efficient way. The results of numerical experiments are quite promising and show that the trigonometric Fourier collocation methods are significantly more efficient in comparison with alternative approaches that have previously appeared in the literature., Author(s): Bin Wang[sup.1] [sup.2] , Arieh Iserles[sup.3] , Xinyuan Wu[sup.2] Author Affiliations: (1) School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, Shandong, People's Republic of China (2) Department of [...]

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential […]