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J.-F. Mennemann, A. Jüngel:
"Perfectly matched .ayers versus discrete transparent boundary conditions in quantum device simulations";
in: "ASC Report 43/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 42.

Discrete transparent boundary conditions (DTBC) and the Perfectly Matched Layers (PML) method for the realization of open boundary conditions in quantum device simulations are compared, based on the stationary and time-dependent Schrödinger equation.
The comparison includes scattering state, wave packet, and transient scattering state simulations in one and two space dimensions. The Schr¨odinger equation is discretized by a second-order Crank-Nicolson method in case of DTBC. For the discretization with PML, symmetric second-, fourth, and sixth-order spatial approximations as well as Crank-Nicolson and classical Runge-Kutta time-integration methods are employed. In two space dimensions, a ring-shaped quantum waveguide device is simulated in the stationary and transient regime. As an application, a simulation of the Aharonov-Bohm effect in this
device is performed, showing the excitation of bound states localized in the ring region. The numerical experiments show that the results obtained from PML are comparable to those obtained using DTBC, while keeping the high numerical efficiency and flexibility as
well as the ease of implementation of the former method.

Schrödinger equation, Perfectly Matched Layers, discrete transparent boundary conditions, transient simulations, quantum waveguides, Aharonov-Bohm effect

http://www.asc.tuwien.ac.at/preprint/2013/asc43x2013.pdf