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A discrete exterior calculus approach to quantum transport on surfaces

We address the problem of computing transport observables on arbitrary surfaces. Our approach is based on discrete exterior calculus (DEC) and applies to open quantum systems. The curved system is approximated by a simplicial complex consisting of flat triangles where each vertex is located on a smo...

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Main Author: SILVA, Leon Denis da
Other Authors: MELO, Silvio de Barros
Format: doctoralThesis
Language: por
Published: Universidade Federal de Pernambuco 2020
Subjects:
Mídia e Interação
Cálculo exterior discreto
Espalhamento quântico
Funções de Green recursisvas
Online Access: https://repositorio.ufpe.br/handle/123456789/36046
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spelling ir-123456789-360462020-01-18T05:15:35Z A discrete exterior calculus approach to quantum transport on surfaces SILVA, Leon Denis da MELO, Silvio de Barros MACEDO, Antonio Murilo Santos http://lattes.cnpq.br/2239251029436873 http://lattes.cnpq.br/3847692220708299 http://lattes.cnpq.br/7160030619369816 Mídia e Interação Cálculo exterior discreto Espalhamento quântico Funções de Green recursisvas We address the problem of computing transport observables on arbitrary surfaces. Our approach is based on discrete exterior calculus (DEC) and applies to open quantum systems. The curved system is approximated by a simplicial complex consisting of flat triangles where each vertex is located on a smooth surface. Was developed a discretization of Schrödinger equation and the associated Green’s functions. Such an approach allowed for the formulation of the tight-binding Hamiltonian based in discrete calculus exterior. We present an efficient algorithm for the calculation of the recursive Green’s functions using numerical tools available for DEC. In addition to working with curved surfaces, our discretization shares the advantages of the Finite Differences Method when submitted to mesh in flat space. Our approach is applied to the calculation of the conductance of a non-flat quantum device coupled to electron reservoirs defined on curved surfaces. We found numerical evidence of a curvature induced integrablechaotic crossover. Abordamos o problema de computar observáveis de transporte em superfícies arbitrárias. Nossa abordagem é baseada em cálculo exterior discreto (DEC) e aplica-se a sistemas quânticos abertos. O sistema curvo é aproximado por um simplicial complex que consiste de triângulos planos, onde cada vértice está localizado em uma superfície suave. Foi desenvolvida uma discretização da equação de Schrödinger e das funções de Green associadas. Tal abordagem permitiu a formulação do hamiltoniano, do tipo tight-binding, com base no cálculo exterior discreto. Apresentamos um algoritmo eficiente para o cálculo das curvas recursivas de Green. Além de trabalhar com superfícies curvas, nossa discretização compartilha as vantagens do Método de Diferenças Finitas quando submetido a um domínio plano, nossa abordagem é aplicada ao cálculo da condutância de um dispositivo curvo acoplado a reservatórios de elétrons definidos em superfícies curvas. Encontramos evidências numéricas de um cruzamento caótico-integrável induzido por curvatura. 2020-01-17T12:12:13Z 2020-01-17T12:12:13Z 2019-10-25 doctoralThesis SILVA, Leon Denis da. A discrete exterior calculus approach to quantum transport on surfaces. 2019. Tese (Doutorado em Ciência da Computação) – Universidade Federal de Pernambuco, Recife, 2019. https://repositorio.ufpe.br/handle/123456789/36046 por openAccess Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ application/pdf Universidade Federal de Pernambuco UFPE Brasil Programa de Pos Graduacao em Ciencia da Computacao
institution REPOSITORIO UFPE
collection REPOSITORIO UFPE
language por
topic Mídia e Interação
Cálculo exterior discreto
Espalhamento quântico
Funções de Green recursisvas
spellingShingle Mídia e Interação
Cálculo exterior discreto
Espalhamento quântico
Funções de Green recursisvas
SILVA, Leon Denis da
A discrete exterior calculus approach to quantum transport on surfaces
description We address the problem of computing transport observables on arbitrary surfaces. Our approach is based on discrete exterior calculus (DEC) and applies to open quantum systems. The curved system is approximated by a simplicial complex consisting of flat triangles where each vertex is located on a smooth surface. Was developed a discretization of Schrödinger equation and the associated Green’s functions. Such an approach allowed for the formulation of the tight-binding Hamiltonian based in discrete calculus exterior. We present an efficient algorithm for the calculation of the recursive Green’s functions using numerical tools available for DEC. In addition to working with curved surfaces, our discretization shares the advantages of the Finite Differences Method when submitted to mesh in flat space. Our approach is applied to the calculation of the conductance of a non-flat quantum device coupled to electron reservoirs defined on curved surfaces. We found numerical evidence of a curvature induced integrablechaotic crossover.
author2 MELO, Silvio de Barros
format doctoralThesis
author SILVA, Leon Denis da
author_sort SILVA, Leon Denis da
title A discrete exterior calculus approach to quantum transport on surfaces
title_short A discrete exterior calculus approach to quantum transport on surfaces
title_full A discrete exterior calculus approach to quantum transport on surfaces
title_fullStr A discrete exterior calculus approach to quantum transport on surfaces
title_full_unstemmed A discrete exterior calculus approach to quantum transport on surfaces
title_sort discrete exterior calculus approach to quantum transport on surfaces
publisher Universidade Federal de Pernambuco
publishDate 2020
url https://repositorio.ufpe.br/handle/123456789/36046
_version_ 1661517183632539648
score 13.657419

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