Simulation of Nanodevices Eigenvalue Problems Based on
Higher-order Symplectic Algorithm

Abstract

Abstract: Numerical solutions of Schr?dinger equation have become increasingly important because of the tremendous demands for the design and optimization of nanodevices where quantum effects are significant or dominate. Using the three-order symplectic integrators and fourth-order collocated spatial differences, a high-order symplectic finite-difference time-domain (SFDTD) scheme is proposed to solve the time-dependent Schr?dinger equation. A detailed numerical study on 1D quantum eigenvalue problems is carried out. Compared with FDTD(2,2) and FDTD(2,4), the simulation results of quantum wells and harmonic oscillators strongly confirm that the explicit SFDTD scheme is well suited for a long-term simulation.

Key words: quantum optics, symplectic integrators, finite-difference time-domain, Schr?dinger equation, nanodevices eigenvalue problems

CLC Number:

O641

SHEN Jing，KUANG Xiao Jing，ZHANG Liang，Cao Xin Yuan, Chen Ming Sheng, Zhang Zhong Xiang . Simulation of Nanodevices Eigenvalue Problems Based on Higher-order Symplectic Algorithm [J]. J4, 2014, 31(3): 340-347.

References

[1] Datta S., Quantum Transport: Atom to Transistor
[M], Cambridge University Press, 2005, New York.
[2] Griffiths D.J., Introduction to Quantum Mechanics
[M], Second Edition Addison-Wesley, 2004, Boston.
[3] Joe Y.S., Satanin A.M., Kim C.S., Classical analogy of Fano resonances
[J], Phys. Scr., 2006, 74 :259-266.
[4] Soriano A., Navarro E.A., Porti J.A., Such V., Analysis of the finite difference time domain technique to solve the Schrodinger equation for quantum devices
[J], J. Appl. Phys., 2004, 95 8011-8018.
[5] Sullivan D.M., Citrin D.S., Determining quantum eigenfunctions in three-dimensional nanoscale structures
[J], J. Appl. Phys., 2005, 97(10): 104305 - 104305-6.
[6] 文舸一, 1999,辛算法及其在电磁场方程中的应用
[J],微波学报, 15(1): 68 - 78. K. Y. Wen, Symplectic algorithm and its application in the electromagnetic field equations
[J], Microwave Journal, 1996, 15(1):68-78.
[7] 冯康,等, 2003,哈密尔顿系统的辛几何算法
[M],杭州:浙江科学技术出版社, 358 - 359. K. Feng, Symplectic algorithm in Hamilton system
[M], Zhejiang Science and Technology Publishing House: 358-359.
[8] G. B. Ren and J. M. Rorison, Eigenvalue problem of the Schrodinger equation via the finite-difference time-domain method
[J], Physical Review E, 2004，69: 036705-1-4
[9] Hanquan Wang, Numerical studies on the split-step finite difference method for nonlinear Schrodinger equations
[J], Applied Mathematics and Computation, 2005, 170: 17–35
[10] 简荣华, 赵翠兰，半导体量子阱中强耦合磁极化子的性质
[J], 量子电子学报，2010, 27 (4): 485–490. H. R. Jan, C. L. Zhao，The property of strong coupling magnetopolaron in semicoductor quantum wells, Chinese Journal of quantum electronics, 2010, 27(4):485-490.

[1]	CHEN Liying , HUANG Kun , WANG Qi , YAN Shinong . Design of an integrated vibration detection module based on diamond NV color centers [J]. Chinese Journal of Quantum Electronics, 2023, 40(4): 500-509.
[2]	BAI Hailong , BAI Jinhai , HU Dong , WANG Yu . Design and implementation of a compact microwave synthesizer for atomic interference gravimeter [J]. Chinese Journal of Quantum Electronics, 2023, 40(4): 510-518.
[3]	LI Songsong. Effects of three-body and four-body interactions on spin squeezing and quantum entanglement in Bose-Einstein condensates [J]. Chinese Journal of Quantum Electronics, 2023, 40(4): 519-527.
[4]	LI Yan , . Correlation properties of Bose⁃Fermi mixture with one⁃dimensional strong interaction [J]. Chinese Journal of Quantum Electronics, 2023, 40(4): 528-540.
[5]	WANG Sheng , FANG Xiaoming , LIN Yu , ZHANG Tianbing , FENG Bao , YU Yang , WANG Le . Four-intensity decoy-state phase-matching quantum key distribution [J]. Chinese Journal of Quantum Electronics, 2023, 40(4): 541-545.
[6]	SUN Yishi , SUN Yi . Parameter prediction of classical-quantum signals co-fiber transmission system based on BP neural network [J]. Chinese Journal of Quantum Electronics, 2023, 40(4): 546-559.
[7]	QI Zhiming , LIANG Wenyao . Influence of beam polarizations on holographic fabrication of compound photonic crystals [J]. Chinese Journal of Quantum Electronics, 2023, 40(4): 447-457.
[8]	DONG Qinlu, HAN Yiping ∗ , ZHANG Qifan. Transmission characteristics of terahertz waves in a hypersonic target plasma sheath [J]. Chinese Journal of Quantum Electronics, 2023, 40(2): 258-266.
[9]	HE Yefeng , , LI Lina ∗ , BAI Qian , CHEN Sihao , QIANG Yuwei . Quantum key distribution of detector’s dead time in heralded single photon source [J]. Chinese Journal of Quantum Electronics, 2023, 40(1): 112-119.
[10]	TAN Zhijie , YANG Hairui , , YU Hong , , HAN Shensheng , ∗. Progress on X-ray diffraction imaging via intensity correlation [J]. Chinese Journal of Quantum Electronics, 2022, 39(6): 851-862.
[11]	LIN Huizu , ∗ , LIU Weitao , ∗ , SUN Shuai , , DU Longkun , , CHANG Chen , , LI Yuegang , . Progress of algorithms used in ghost imaging [J]. Chinese Journal of Quantum Electronics, 2022, 39(6): 863-879.
[12]	WANG Xiaoyan, WANG Zhiyuan, CHEN Ziyang, PU Jixioing ∗. Detection of orbital angular momentum of multiple vortices from speckle via deep learning [J]. Chinese Journal of Quantum Electronics, 2022, 39(6): 955-961.
[13]	LI Nengfei , SUN Yusong , , HUANG Jian , ∗. Research on cosine encoded multiplexing high spatial resolution ghost imaging [J]. Chinese Journal of Quantum Electronics, 2022, 39(6): 973-982.
[14]	DAI Pan, PANG Zhiguang, LI Jian, WANG Qin ∗. Nonlinear Bell inequality based on entanglement sources [J]. Chinese Journal of Quantum Electronics, 2022, 39(5): 761-767.
[15]	ZHOU Xiantao, JIANG Yinghua ∗ , GUO Chenfei, ZHAO Ning, LIU Biao. Quantum secure direct communication protocol based on mixture of GHZ particles and single photon [J]. Chinese Journal of Quantum Electronics, 2022, 39(5): 768-775.

Simulation of Nanodevices Eigenvalue Problems Based on Higher-order Symplectic Algorithm

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments