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Time-dependent simulations of quantum waveguides using a time-splitting spectral method

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  • Jüngel, Ansgar
  • Mennemann, Jan-Frederik

Abstract

The electron flow through quantum waveguides is modeled by the time-dependent Schrödinger equation with absorbing boundary conditions, which are realized by a negative imaginary potential. The Schrödinger equation is discretized by a time-splitting spectral method, and the quantum waveguides are fed by a mono-energetic incoming plane wave pulse. The resulting algorithm is extremely efficient due to the Fast Fourier Transform implementation of the spectral scheme. Numerical convergence rates for a one-dimensional scattering problem are calculated. The transmission rates of a two-dimensional T-stub quantum waveguide and a single-branch coupler are numerically computed. Moreover, the transient behavior of a three-dimensional T-stub waveguide is simulated.

Suggested Citation

  • Jüngel, Ansgar & Mennemann, Jan-Frederik, 2010. "Time-dependent simulations of quantum waveguides using a time-splitting spectral method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 883-898.
    • Handle: RePEc:eee:matcom:v:81:y:2010:i:4:p:883-898
    DOI: 10.1016/j.matcom.2010.09.013
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    References listed on IDEAS

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    1. Arnold, Anton & Schulte, Maike, 2008. "Transparent boundary conditions for quantum-waveguide simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 898-905.
    2. Shin, Mincheol, 2008. "Three-dimensional quantum simulation of multigate nanowire field effect transistors," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1060-1070.
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