Abstract
Abstract : The Wigner formalism has previously been applied by numerous groups to analyze the steady-state behavior of particle transport within open quantum systems. In particular, the Wigner-Poisson model has been used as a tool to study electron transport through double-barrier resonant tunneling diodes (RTDs) with open boundary conditions. The goals of this project is to study stability and physical accuracy of numerical solutions to the Wigner-Poisson model. Numerous authors who simulated RTD with the Wigner-Poisson model assumed that the discrete Wigner function is periodic in momentum space. The periodicity follows from the Fourier transform of the density matrix. The inverse Fourier transform provides us with the important proof that the number of spatial intervals is equal to the number of intervals in the momentum space. In addition we obtain that the step size in the momentum space does not depend on the number of intervals. As a result the number of relevant intervals in the momentum space does not also depend on the total number of intervals. Stability of algorithms used by different authors is investigated. The analysis of the stability shows that Greg Recine has used unstable algorithm.
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