Details
| Original language | English |
|---|---|
| Pages (from-to) | 89-103 |
| Number of pages | 15 |
| Journal | Journal of Computational Physics |
| Volume | 226 |
| Issue number | 1 |
| Publication status | Published - 9 Apr 2007 |
| Externally published | Yes |
Abstract
Numerical methods for calculating strong-field, nonperturbative electron dynamics are investigated. Two different quantum-mechanical approaches are discussed: the time-dependent Schrödinger equation and time-dependent density functional theory. We show that when solving the time-dependent Schrödinger equation, small errors in the initial ground-state wave function can be magnified considerably during propagation. A scheme is presented to efficiently obtain the ground state with high accuracy. We further demonstrate that the commonly-used absorbing boundary conditions can severely influence the results. The requirements on the boundary conditions are somewhat less stringent in effective single-particle approaches such as time-dependent density functional theory. We point out how results from accurate wave-function based calculations can be used to improve the density functional description of long-ranged, nonlinear electron dynamics. We present details of a method to reconstruct, numerically, the full, unapproximated, Kohn-Sham potential from the density and current of the exact system.
Keywords
- Density functional theory, Exchange-correlation potential, Real-space methods, Strong-field ionization, Time-dependent Schrödinger equation
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Computational Physics, Vol. 226, No. 1, 09.04.2007, p. 89-103.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Numerical aspects of real-space approaches to strong-field electron dynamics
AU - de Wijn, Astrid S.
AU - Kümmel, Stephan
AU - Lein, Manfred
N1 - Funding Information: S.K. acknowledges discussions with E.K.U. Gross, T. Kirchner, M. Mundt and financial support by the Deutsche Forschungsgemeinschaft. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2007/4/9
Y1 - 2007/4/9
N2 - Numerical methods for calculating strong-field, nonperturbative electron dynamics are investigated. Two different quantum-mechanical approaches are discussed: the time-dependent Schrödinger equation and time-dependent density functional theory. We show that when solving the time-dependent Schrödinger equation, small errors in the initial ground-state wave function can be magnified considerably during propagation. A scheme is presented to efficiently obtain the ground state with high accuracy. We further demonstrate that the commonly-used absorbing boundary conditions can severely influence the results. The requirements on the boundary conditions are somewhat less stringent in effective single-particle approaches such as time-dependent density functional theory. We point out how results from accurate wave-function based calculations can be used to improve the density functional description of long-ranged, nonlinear electron dynamics. We present details of a method to reconstruct, numerically, the full, unapproximated, Kohn-Sham potential from the density and current of the exact system.
AB - Numerical methods for calculating strong-field, nonperturbative electron dynamics are investigated. Two different quantum-mechanical approaches are discussed: the time-dependent Schrödinger equation and time-dependent density functional theory. We show that when solving the time-dependent Schrödinger equation, small errors in the initial ground-state wave function can be magnified considerably during propagation. A scheme is presented to efficiently obtain the ground state with high accuracy. We further demonstrate that the commonly-used absorbing boundary conditions can severely influence the results. The requirements on the boundary conditions are somewhat less stringent in effective single-particle approaches such as time-dependent density functional theory. We point out how results from accurate wave-function based calculations can be used to improve the density functional description of long-ranged, nonlinear electron dynamics. We present details of a method to reconstruct, numerically, the full, unapproximated, Kohn-Sham potential from the density and current of the exact system.
KW - Density functional theory
KW - Exchange-correlation potential
KW - Real-space methods
KW - Strong-field ionization
KW - Time-dependent Schrödinger equation
UR - http://www.scopus.com/inward/record.url?scp=34548438429&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2007.03.022
DO - 10.1016/j.jcp.2007.03.022
M3 - Article
AN - SCOPUS:34548438429
VL - 226
SP - 89
EP - 103
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
IS - 1
ER -