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A Discrete Exterior Calculus Approach to Quantum Transport and Quantum Chaos on Surface

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We address the problem of computing transport observables and spectral characteristics of quantum dynamics on arbitrary surfaces. Our approach is based on discrete exterior calculus (DEC) and applies to both open and closed quantum systems. We present an efficient algorithm for the calculation of the recursive Green’s functions (for open systems) and the full set of eigenfunctions and eigenvalues (for closed systems) using numerical tools available for DEC. Our approach is applied to the calculation of the conductance of a non-flat quantum device coupled to electron reservoirs and to obtain the spectra of ballistic cavities defined on curved surfaces. In both cases we found numerical evidences of a curvature induced integrable-chaotic crossover.
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Keywords: Discrete Exterior Calculus; Quantum Chaos; Quantum Transport; Recursive Green’s Function

Document Type: Research Article

Affiliations: 1: Centro de Informática, Universidade Federal de Pernambuco, Recife, PE, 50670-901, Brazil 2: Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, Recife, PE, 50670-901, Brazil 3: Departamento de Estatística e Informática, Universidade Federal Rural de Pernambuco, Recife, PE, 52171-900, Brazil

Publication date: September 1, 2019

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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