ALmost EXact boundary conditions for transient Schrödinger–Poisson system

Journal Article · Sun May 15 00:00:00 EDT 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2016.02.025· OSTI ID:22572298

Bian, Lei ^[1]; Pang, Gang ^[2]; Tang, Shaoqiang ^[1]; Arnold, Anton ^[3]

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1. HEDPS, CAPT, College of Engineering, Peking University, Beijing 100871 (China)
2. Institute of Applied Physics and Computational Mathematics, Beijing 100088 (China)
3. Institut für Analysis und Scientific Computing, TU-Wien, Wiedner Hauptstr. 8, 1040 Wien (Austria)

For the Schrödinger–Poisson system, we propose an ALmost EXact (ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank–Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. [1], yet at a much reduced complexity. Primary peaks in wave function profile appear as a consequence of quantum resonance, and should be considered in selecting the cut-off wave number for numerical simulations.

• OSTI ID: 22572298
• Journal Information: Journal of Computational Physics, Vol. 313; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
BOUNDARY CONDITIONS
COMPUTERIZED SIMULATION
PEAKS
TRANSIENTS
TUNNEL DIODES
TUNNEL EFFECT
WAVE FUNCTIONS