Loading [MathJax]/jax/output/HTML-CSS/config.js
full
search.png

Search

close.png

Cancel

arrow
Volume 16, Issue 3
Green Function Method for Quantum Transport Based on the Generalized Fourier Transform

Haiyan Jiang, Xingming Gao, Yueguang Hu & Tiao Lu

DOI: 10.4208/nmtma.OA-2022-0164

Numer. Math. Theor. Meth. Appl., 16 (2023), pp. 701-719.

Published online: 2023-08

Preview Purchase PDF 2144 23945

Cited by

google scholar semantic scholar
Export citation
  • Abstract

The rigorous relations between the propagators of transient Schrödinger equations and stationary Green functions are established. Based on the generalized Fourier transform, non-singular transparent boundary condition for transient problem is proposed in a representation of Green functions. The unified framework of Green function method is presented for converting an open boundary problem into a bounded boundary problem. Numerical scheme for time-dependent Schrödinger equation with non-singular transparent boundary condition is designed to simulate the propagations of a free Gaussian wave packet and the resonant tunnelling through double barriers. Numerical results validate the effectiveness of non-singular transparent boundary condition.

  • Keywords

Schrödinger equation, Green function, generalized Fourier transform, transparent boundary condition.

  • AMS Subject Headings

42A38, 65M80, 81-10, 81U26

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-16-701, author = {Jiang , HaiyanGao , XingmingHu , Yueguang and Lu , Tiao}, title = {Green Function Method for Quantum Transport Based on the Generalized Fourier Transform}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2023}, volume = {16}, number = {3}, pages = {701--719}, abstract = {

The rigorous relations between the propagators of transient Schrödinger equations and stationary Green functions are established. Based on the generalized Fourier transform, non-singular transparent boundary condition for transient problem is proposed in a representation of Green functions. The unified framework of Green function method is presented for converting an open boundary problem into a bounded boundary problem. Numerical scheme for time-dependent Schrödinger equation with non-singular transparent boundary condition is designed to simulate the propagations of a free Gaussian wave packet and the resonant tunnelling through double barriers. Numerical results validate the effectiveness of non-singular transparent boundary condition.

}, issn = {2079-7338}, doi = {https://doi.org/ 10.4208/nmtma.OA-2022-0164}, url = {http://global-sci.org/intro/article_detail/nmtma/21963.html} }
TY - JOUR T1 - Green Function Method for Quantum Transport Based on the Generalized Fourier Transform AU - Jiang , Haiyan AU - Gao , Xingming AU - Hu , Yueguang AU - Lu , Tiao JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 701 EP - 719 PY - 2023 DA - 2023/08 SN - 16 DO - http://doi.org/ 10.4208/nmtma.OA-2022-0164 UR - https://global-sci.org/intro/article_detail/nmtma/21963.html KW - Schrödinger equation, Green function, generalized Fourier transform, transparent boundary condition. AB -

The rigorous relations between the propagators of transient Schrödinger equations and stationary Green functions are established. Based on the generalized Fourier transform, non-singular transparent boundary condition for transient problem is proposed in a representation of Green functions. The unified framework of Green function method is presented for converting an open boundary problem into a bounded boundary problem. Numerical scheme for time-dependent Schrödinger equation with non-singular transparent boundary condition is designed to simulate the propagations of a free Gaussian wave packet and the resonant tunnelling through double barriers. Numerical results validate the effectiveness of non-singular transparent boundary condition.

Jiang , HaiyanGao , XingmingHu , Yueguang and Lu , Tiao. (2023). Green Function Method for Quantum Transport Based on the Generalized Fourier Transform. Numerical Mathematics: Theory, Methods and Applications. 16 (3). 701-719. doi: 10.4208/nmtma.OA-2022-0164
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard