研究一种准确、有效的数值方法是现代纳米器件建模和优化的重要目标之一,而分析大多数纳米器件特性的起始点是确定器件的本征值和本征态.提出了一种新算法一高阶辛时域有限差分法(Symplectic finitedifference time-domain,SFDTD(3,4)),求解含时薛定谔方程.在时间上采用三阶辛积分,空间上采用四阶差分格式,建立了针对含时薛定谔方程数值求解的高阶辛时域有限差分算法.将高阶辛算法SFDTD(3,4)用于一维量子阱中盒中粒子和一维谐振子的仿真中,实验结果表明SFDTD(3,4)法比传统的时域有限差分算法以及高阶时域有限差分算法更加准确,适用于对纳米器件本征问题的长时间仿真.
参考文献
| [1] | Datta S.Quantum Transport:Atom to Transistor[M].New York:Cambridge University Press,2005. |
| [2] | Griffiths D J.Introduction to Quantum Mechanics[M].2nd Edi.,Boston:Addison-Wesley,2004. |
| [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,et al.Analysis of the finite difference time domain technique to solve the Schr(o)dinger 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] | Wen K Y.Symplectic algorithm and its application in the electromagnetic field equations[J].Microwave Journal (微波学报),1996,15(1):68-78 (in Chinese). |
| [7] | Feng K,et al.Symplectic Algorithm in Hamilton System(哈密尔顿系统的辛几何算法)[M].Hangzhou:Zhejiang Science and Technology Publishing House,2003:358-359 (in Chinese). |
| [8] | Ren G B,Rorison J M.Eigenvalue problem of the Schr(o)dinger equation via the finite-difference time-domain method[J].Physical Review E,2004,69:036705-1-4. |
| [9] | Wang Hanquan.Numerical studies on the split-step finite difference method for nonlinear Schr(o)dinger equations[J].Applied Mathematics and Computation,2005,170:17-35. |
| [10] | Jan H R,Zhao C L.The property of strong coupling magnetopolaron in semicoductor quantum wells[J].Chinese Journal of Quantum Electronics(量子电子学报),2010,27(4):485-490 (in Chinese). |
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