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Frozen Gaussian approximation-based two-level methods for multi-frequency Schrodinger equation
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DOI：10.1016/j.cpc.2016.05.023.png)
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In this paper, we develop two-level numerical methods for the time-dependent Schrodinger equation (TDSE) in multi-frequency regime. This work is motivated by attosecond science (Corkum and Krausz, 2007), which refers to the interaction of short and intense laser pulses with quantum particles generating wide frequency spectrum light, and allowing for the coherent emission of attosecond pulses (1 attosecond = 10(-18) s). The principle of the proposed methods consists in decomposing a wavefunction into a low/moderate frequency (quantum) contribution, and a high frequency contribution exhibiting a semi-classical behavior. Low/moderate frequencies are computed through the direct solution to the quantum TDSE on a coarse mesh, and the high frequency contribution is computed by frozen Gaussian approximation (Herman and Kluk, 1984). This paper is devoted to the derivation of consistent, accurate and efficient algorithms performing such a decomposition and the time evolution of the wavefunction in the multi-frequency regime. Numerical simulations are provided to illustrate the accuracy and efficiency of the derived algorithms. (C) 2016 Elsevier B.V. All rights reserved.
Keyword:
Geometric optics
Frozen Gaussian approximation
Schrodinger equation
Multilevel method
Attosecond science
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3.4
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1.2W
被引数:
3.7W
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