Long-time solution of the time-dependent Schrödinger equation for an atom in an electromagnetic field using complex coordinate contours

Tao, Liang; Vanroose, Wim; Reps, Bram; Rescigno, T. N.; McCurdy, C. William

doi:10.1103/physreva.80.063419

Cited by 25 publications

(48 citation statements)

References 34 publications

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“…This is a plausible possibility, as analyticity plays a crucial role for ECS and small integration errors by using Lobatto quadrature instead of evaluating integrals exactly might destroy perfect absorption. Now we show that this speculation was incorrect, that FEM-DVR gives numerical results of the same quality as FEM, and that the problems encountered in [19] must have had a different origin.…”

Section: Ecs and Irecs For A Fem-dvr Gridmentioning

confidence: 86%

“…[19] the infinite range idea was not used. However, at some expense as to efficiency, also a standard DVR discretization using only polynomials without exponential damping produces highly accurate results.…”

Section: Discussion and Conclusion On Fem-dvrmentioning

confidence: 99%

“…One sees that errors can be very well controlled and no artifacts appear also in the area |x| ∼ R 0 . In spite of similar discretization sizes, the calculations in [19] were reported to be instable, especially near |x| = R 0 .…”

Section: Discussion and Conclusion On Fem-dvrmentioning

confidence: 99%

“…[19] severe instabilities were reported for ECS absorption using FEM-DVR discretization for a simple test-problem where the irECS showed perfect absorption.…”

Section: Ecs and Irecs For A Fem-dvr Gridmentioning

confidence: 96%

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Perfect absorption in Schrödinger-like problems using non-equidistant complex grids

Weinmüller

Rohland

et al. 2017

Journal of Computational Physics

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Section: Ecs and Irecs For A Fem-dvr Gridmentioning

confidence: 86%

Section: Discussion and Conclusion On Fem-dvrmentioning

confidence: 99%

Section: Discussion and Conclusion On Fem-dvrmentioning

confidence: 99%

“…[19] severe instabilities were reported for ECS absorption using FEM-DVR discretization for a simple test-problem where the irECS showed perfect absorption.…”

Section: Ecs and Irecs For A Fem-dvr Gridmentioning

confidence: 96%

See 2 more Smart Citations

Perfect absorption in Schrödinger-like problems using non-equidistant complex grids

Weinmüller

Rohland

et al. 2017

Journal of Computational Physics

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“…Among the different techniques implemented to compute the resonance energies established methods are the complex scaling [28][29][30], and exterior complex scaling [31]; the latter was introduced as an extension of the former method. These have been widely used in scattering problems [29,30], and also in time-dependent Schrödinger equation problems for strong fields [32][33][34]. For our aim of studying the field ionization properties of H 2 O orbitals, we implement a modified exterior complex scaling technique in which the radial coordinates are extended into the complex plane by a phase factor, which is turned on gradually beyond some distance from the origin.…”

Section: Exterior Complex Scalingmentioning

confidence: 99%

Calculation of Stark resonance parameters for valence orbitals of the water molecule

Laso

Horbatsch

2016

Phys. Rev. A

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An exterior complex scaling technique is applied to compute Stark resonance parameters for two molecular orbitals (1b 1 and 1b 2 ) represented in the field-free limit in a single-center expansion. For electric DC field configurations that guarantee azimuthal symmetry of the solution the calculation is carried out by solving a two-dimensional partial differential equation in spherical polar coordinates using a finite-element method. The resonance positions and widths as a function of electric field strengths are shown for field strengths starting in the tunnelling ionization regime, and extending well into the over-barrier ionization region.

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Finite‐Difference Time‐Domain Simulation of Strong‐Field Ionization: A Perfectly Matched Layer Approach

Kamban

Christensen

Søndergaard

et al. 2020

Physica Status Solidi (b)

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A finite-difference time-domain (FDTD) scheme with perfectly matched layers (PMLs) is considered for solving the time-dependent Schrödinger equation and simulating the laser-induced ionization of two systems: 1) an electron initially bound to a 1D δ potential and 2) excitons in carbon nanotubes (CNTs). The performance of PMLs based on different absorption functions is compared, where slowly growing functions are found to be preferable. PMLs are shown to be able to reduce the computational domain, and thus the required numerical resources, by several orders of magnitude. This is demonstrated by testing the proposed method against an FDTD approach without PMLs and a very large computational domain. It is shown that PMLs outperform the well-known exterior complex scaling (ECS) technique for short-range potentials when implemented in FDTD. For long-range potentials such as in CNTs, however, ECS performs better than PMLs when propagating over many periods.

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Long-time solution of the time-dependent Schrödinger equation for an atom in an electromagnetic field using complex coordinate contours

Cited by 25 publications

References 34 publications

Perfect absorption in Schrödinger-like problems using non-equidistant complex grids

Perfect absorption in Schrödinger-like problems using non-equidistant complex grids

Calculation of Stark resonance parameters for valence orbitals of the water molecule

Finite‐Difference Time‐Domain Simulation of Strong‐Field Ionization: A Perfectly Matched Layer Approach

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