Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

doi:10.1088/1674-1056/ac11d6

中国物理B ›› 2022, Vol. 31 ›› Issue (1): 13201-013201.doi: 10.1088/1674-1056/ac11d6

Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

Shun Wang(王顺) and Wei-Chao Jiang(姜维超)^†

College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China

收稿日期:2021-04-03 修回日期:2021-06-04 接受日期:2021-07-07 出版日期:2021-12-03 发布日期:2021-12-28
通讯作者: Wei-Chao Jiang E-mail:jiang.wei.chao@szu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12074265 and 11804233).

Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

Shun Wang(王顺) and Wei-Chao Jiang(姜维超)^†

College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China

Received:2021-04-03 Revised:2021-06-04 Accepted:2021-07-07 Online:2021-12-03 Published:2021-12-28
Contact: Wei-Chao Jiang E-mail:jiang.wei.chao@szu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12074265 and 11804233).

摘要/Abstract

摘要： We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schrödinger equation of the single-active-electron atom in the field of laser pulses by combining smooth exterior complex scaling (SECS) absorbing method and Arnoldi propagation method. Such combination has not been reported in the literature. The proposed scheme is particularly useful in the applications involving long-time wave propagation. The SECS is a wonderful absorber, but its application results in a non-Hermitian Hamiltonian, invalidating propagators utilizing the Hermitian symmetry of the Hamiltonian. We demonstrate that the routine Arnoldi propagator can be modified to treat the non-Hermitian Hamiltonian. The efficiency of the proposed scheme is checked by tracking the time-dependent electron wave packet in the case of both weak extreme ultraviolet (XUV) and strong infrared (IR) laser pulses. Both perfect absorption and stable propagation are observed.

关键词: time-dependent Schrö, dinger equation (TDSE), smooth exterior complex scaling (SECS) absorbing method, Arnoldi propagator

Abstract: We develop a highly efficient scheme for numerically solving the three-dimensional time-dependent Schrödinger equation of the single-active-electron atom in the field of laser pulses by combining smooth exterior complex scaling (SECS) absorbing method and Arnoldi propagation method. Such combination has not been reported in the literature. The proposed scheme is particularly useful in the applications involving long-time wave propagation. The SECS is a wonderful absorber, but its application results in a non-Hermitian Hamiltonian, invalidating propagators utilizing the Hermitian symmetry of the Hamiltonian. We demonstrate that the routine Arnoldi propagator can be modified to treat the non-Hermitian Hamiltonian. The efficiency of the proposed scheme is checked by tracking the time-dependent electron wave packet in the case of both weak extreme ultraviolet (XUV) and strong infrared (IR) laser pulses. Both perfect absorption and stable propagation are observed.

Key words: time-dependent Schrö, dinger equation (TDSE), smooth exterior complex scaling (SECS) absorbing method, Arnoldi propagator

中图分类号: (Photoionization of atoms and ions)

32.80.Fb

33.20.Xx (Spectra induced by strong-field or attosecond laser irradiation) 31.15.A- (Ab initio calculations)

Shun Wang(王顺) and Wei-Chao Jiang(姜维超). Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator[J]. 中国物理B, 2022, 31(1): 13201-013201.

Shun Wang(王顺) and Wei-Chao Jiang(姜维超). Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator[J]. Chin. Phys. B, 2022, 31(1): 13201-013201.

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Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

Solving the time-dependent Schrödinger equation by combining smooth exterior complex scaling and Arnoldi propagator

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