Efficient computation of Wigner-Eisenbud functions

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• 作者：Bahaaudin M. Raffah^a ; ^b ; ^{10571115@student.uwa.edu.au} ; ^{Braffah2003@yahoo.com} ; Paul C. Abbott^a ; ^{paul.c.abbott@uwa.edu.au}
• 关键词：Wigner&ndash ; Eisenbud functions ; Discrete cosine transform (DCT) ; Semiconductor heterostructures ; Quantum transport ; Cylindrical nanowires
• 刊名：Computer Physics Communications
• 出版年：2013
• 出版时间：June, 2013
• 年：2013
• 卷：184
• 期：6
• 页码：1581-1591
• 全文大小：1078 K

文摘

The -matrix method, introduced by Wigner and Eisenbud (1947) , has been applied to a broad range of electron transport problems in nanoscale quantum devices. With the rapid increase in the development and modeling of nanodevices, efficient, accurate, and general computation of Wigner-Eisenbud functions is required. This paper presents the Mathematica package WignerEisenbud, which uses the Fourier discrete cosine transform to compute the Wigner-Eisenbud functions in dimensionless units for an arbitrary potential in one dimension, and two dimensions in cylindrical coordinates.

Program summary

Program title: WignerEisenbud

Catalogue identifier: AEOU_v1_0

Program summary URL:

Program obtainable from: CPC Program Library, Queen¡¯s University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence,

Distribution format: tar.gz

Programming language: Mathematica

Operating system: Any platform supporting Mathematica 7.0 and above

Keywords: Wigner-Eisenbud functions, discrete cosine transform (DCT), cylindrical nanowires

Classification: 7.3, 7.9, 4.6, 5

Nature of problem:

Computing the 1D and 2D Wigner-Eisenbud functions for arbitrary potentials using the DCT.

Solution method:

The R-matrix method is applied to the physical problem. Separation of variables is used for eigenfunction expansion of the 2D Wigner-Eisenbud functions. Eigenfunction computation is performed using the DCT to convert the Schr?dinger equation with Neumann boundary conditions to a generalized matrix eigenproblem.

Limitations: Restricted to uniform (rectangular grid) sampling of the potential. In 1D the number of sample points, , results in matrix computations involving matrices.

Unusual features:

Eigenfunction expansion using the DCT is fast and accurate. Users can specify scattering potentials using functions, or interactively using mouse input. Use of dimensionless units permits application to a wide range of physical systems, not restricted to nanoscale quantum devices.

Running time: Case dependent.