Multiscale simulation of transport in an open quantum system: Resonances and WKB interpolation

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• 作者：Naoufel Ben Abdallah and Olivier Pinaud
• 关键词：Schrö ; dinger equation ; Numerical scheme ; Resonant tunneling diode ; WKB approximation ; Resonant states
• 刊名：Journal of Computational Physics
• 出版年：2006
• 出版时间：20 March 2006
• 年：2006
• 卷：213
• 期：1
• 页码：288-310
• 全文大小：447 K

文摘

A numerical scheme for the one-dimensional stationary Schrödinger–Poisson model is described. The scheme is used to simulate a resonant tunneling diode and provides an important reduction of the simulation time. The improvement is twofold. First the grid spacing in the position variable is made coarser by using oscillating interpolation functions derived from the WKB asymptotics. Then the discretization of the energy variable, which is a parameter for the Schrödinger equation, is improved by approaching the wavefunctions in the double barrier region by its projection on the resonant states (following the work of Presilla–Sjöstrand and Jona-Lasinio [On Schrödinger equations with concentrated non-linearities, Ann. Phys. 240 (1995) 1–21]).