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Résumé
The transfermatrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schrödinger's equation, in situations where the solutions of interest are in the continuous part of the energy spectrum. The technique is actually a generalization in three dimensions of methods used to obtain scattering solutions in one dimension. Using the layeraddition algorithm allows one to control the stability of the computation and to describe efficiently periodic repetitions of a basic unit. This paper, which is an update of an article originally published in Physical and Chemical News 16, 4653 (2004), provides a pedagogical presentation of this technique. It describes in details how the band structure associated with an infinite periodic medium can be extracted from the transfer matrices that characterize a single basic unit. The
method is applied to the calculation of the transmission and band structure of electrons subject to cosine potentials in a cylindrical wire. The simulations show that bound states must be considered because of their impact as sharp resonances in the transmission probabilities and to remove unphysical discontinuities in the band structure. Additional states only improve the completeness of the representation.
method is applied to the calculation of the transmission and band structure of electrons subject to cosine potentials in a cylindrical wire. The simulations show that bound states must be considered because of their impact as sharp resonances in the transmission probabilities and to remove unphysical discontinuities in the band structure. Additional states only improve the completeness of the representation.
langue originale  Anglais 

Numéro d'article  1907.06940 
Nombre de pages  13 
journal  ArXiv preprint 
Etat de la publication  Publié  16 juil. 2019 
motsclés
 transfer matrix
 bound states
 band structure
 electronic transport
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CÉCI – Consortium des Équipements de Calcul Intensif
CHAMPAGNE, B., Lazzaroni, R., Geuzaine , C., Chatelain, P. & Knaepen, B.
1/01/18 → 31/12/22
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Plateforme Technologique Calcul Intensif
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