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Transparent Boundary Conditions for Quantum-Waveguide Simulations

Summary: Transparent Boundary Conditions for
Quantum-Waveguide Simulations
Anton Arnold1
, Maike Schulte2
1Institut f¨ur Analysis und Scientific Computing, Technische Universit¨at Wien,
Wiedner Hauptstr. 8, A­1040 Wien, Austria;
2Institut f¨ur Numerische und Angewandte Mathematik, Universit¨at M¨unster,
Einsteinstr. 62, D­48149 M¨unster, Germany
We consider the two-dimensional, time-dependent Schr¨odinger equation discretized
with the Crank-Nicolson finite difference scheme. For this difference equation we
derive discrete transparent boundary conditions (DTBCs) in order to get highly
accurate solutions for open boundary problems. We apply inhomogeneous DTBCs
to the transient simulation of quantum waveguides with a prescribed electron inflow.
Key words:
Quantum waveguide, Schr¨odinger equation, transparent boundary condition, finite
difference scheme
1 Introduction
Quantum waveguides are novel electronic switches of nanoscale dimensions.
They are made of several different semiconductor materials such that the


Source: Arnold, Anton - Institut für Analysis und Scientific Computing, Technische Universität Wien


Collections: Mathematics