Paper Info
Title
Frozen Gaussian approximation-based two-level methods for multi-frequency Schrödinger equation.
Abstract
In this paper, we develop two-level numerical methods for the time-dependent Schrödinger 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.
Year
DOI
Venue
2016
10.1016/j.cpc.2016.05.023
Computer Physics Communications
Keywords
Field
DocType
Geometric optics,Frozen Gaussian approximation,Schrödinger equation,Multilevel method,Attosecond science
Attosecond,Quantum,Computational physics,Mathematical analysis,Quantum mechanics,Schrödinger equation,Laser,Wave function,Time evolution,Geometrical optics,Numerical analysis,Physics
Journal
Volume
ISSN
Citations 
207
0010-4655
0
PageRank 
References 
Authors
0.34
4
2
Name
Order
Citations
PageRank
Emmanuel Lorin15513.13
Xu Yang2459.17