Exponential Propagators (Integrators) for the Time-Dependent Schrödinger Equation

Bandrauk, André D.; Lu, Hui

doi:10.1142/s0219633613400014

Cited by 61 publications

(43 citation statements)

References 82 publications

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“…(1), thus providing initial states which are eigenstates of the grid. 45 The molecular ionization potential energies for the three lowest electronic states are, respectively, I p (1sσ g ) = 1.08 a.u., I p (2pσ u ) = 0.65 a.u., and I p (2pπ u ) = 0.43 a.u. It has been shown that MPADs exhibit a rotation angle with respect to the molecular and laser polarization axes, which mainly arises from the effects of the nonspherical asymmetric molecular Coulomb potential and the helicity of the ionizing photons.…”

Section: Resultsmentioning

confidence: 99%

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Molecular photoelectron angular distribution rotations in multi-photon resonant ionization of H2+ by circularly polarized ultraviolet laser pulses

Yuan

Chelkowski

Bandrauk

2015

The Journal of Chemical Physics

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We study effects of pulse durations on molecular photoelectron angular distributions (MPADs) in ultrafast circular polarization ultraviolet resonant ionization processes. Simulations performed on aligned H2 (+) by numerically solving time dependent Schrödinger equations show rotations of MPADs with respect to the molecular symmetry axes. It is found that in multi-photon resonant ionization processes, rotation angles are sensitive to pulse durations, which we attribute to the coherent resonant excitation between the ground state and the intermediate excited electronic state induced by Rabi oscillations. Multi-photon nonresonant and single photon ionization processes are simulated and compared which exhibit a constant rotation angle. An asymmetry parameter is introduced to describe the pulse duration sensitivity by perturbation theory models. Influence of pulse frequency detunings on MPADs is also investigated where oscillations of rotations are absent at long pulse durations due to nonresonance excitation.

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Section: Resultsmentioning

confidence: 99%

“…(1) is solved numerically by a secondorder split-operator method in the time step δt combined with a fifth order finite difference method and Fourier transform technique in the spatial steps δ ρ, δθ, and δz. 28,44,45 The time step is taken to be δt = 0.01 a.u. = 0.24 as, the spatial discretization is δ ρ = δz = 0.25 a.u.…”

Section: Methodsmentioning

confidence: 99%

Molecular photoelectron angular distribution rotations in multi-photon resonant ionization of H2+ by circularly polarized ultraviolet laser pulses

Yuan

Chelkowski

Bandrauk

2015

The Journal of Chemical Physics

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“…The TDSE (2a) was solved using a second-order operator splitting scheme in both 1D and 2D cases [70]. Derivatives of the wave function with respect to the electron position (i.e.…”

Section: Discussionmentioning

confidence: 99%

Classical versus quantum views of intense laser pulse propagation in gases

Berman

Chandre

Dubois

et al. 2019

J. Phys. B: At. Mol. Opt. Phys.

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We study the behavior of reduced models for the propagation of intense laser pulses in atomic gases. The models we consider incorporate ionization, blueshifting, and other nonlinear propagation effects in an ab initio manner, by explicitly taking into account the microscopic electron dynamics. Numerical simulations of the propagation of ultrashort linearly-polarized and elliptically-polarized laser pulses over experimentally-relevant propagation distances are presented. We compare the behavior of models where the electrons are treated classically with those where they are treated quantum-mechanically. A classical equivalent to the ground state is found, which maximizes the agreement between the quantum and classical predictions of the single-atom ionization probability as a function of laser intensity. We show that this translates into quantitative agreement between the quantum and classical models for the laser field evolution during propagation through gases of ground-state atoms. This agreement is exploited to provide a classical perspective on low-and highorder harmonic generation in linearly-polarized fields. In addition, we demonstrate the stability of the polarization of a nearly-linearly-polarized pulse using a two-dimensional model.

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“…We solve the equations of motion Eqs. (7) and (14) using a second-order exponential integrator [44,45]. Equation (7) is integrated as, c (1)…”

Section: Step 3: Computation Of G Lmmentioning

confidence: 99%

Implementation of the multiconfiguration time-dependent Hatree-Fock method for general molecules on a multiresolution Cartesian grid

2016

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We report a three-dimensional numerical implementation of multiconfiguration time-dependent Hartree-Fock (MCTDHF) based on a multi-resolution Cartesian grid, with no need to assume any symmetry of molecular structure. We successfully compute high-harmonic generation (HHG) of H2 and H2O. The present implementation will open a way to the first-principle theoretical study of intense-field and attosecond-pulse induced ultrafast phenomena in general molecules.

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Exponential Propagators (Integrators) for the Time-Dependent Schrödinger Equation

Cited by 61 publications

References 82 publications

Molecular photoelectron angular distribution rotations in multi-photon resonant ionization of H2+ by circularly polarized ultraviolet laser pulses

Molecular photoelectron angular distribution rotations in multi-photon resonant ionization of H2+ by circularly polarized ultraviolet laser pulses

Classical versus quantum views of intense laser pulse propagation in gases

Implementation of the multiconfiguration time-dependent Hatree-Fock method for general molecules on a multiresolution Cartesian grid

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