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Article

Modeling Quantum Dot Systems as Random Geometric Graphs with Probability Amplitude-Based Weighted Links

1
Department of Signal Processing and Communications, University of Alcalá, 28801 Alcalá de Henares, Spain
2
Department of Physics and Mathematics, University of Alcalá, 28801 Alcalá de Henares, Spain
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Author to whom correspondence should be addressed.
Academic Editor: Juan P. Martínez Pastor
Nanomaterials 2021, 11(2), 375; https://doi.org/10.3390/nano11020375
Received: 21 December 2020 / Revised: 18 January 2021 / Accepted: 27 January 2021 / Published: 2 February 2021
(This article belongs to the Special Issue Quantum Dots & Quantum Wells)
This paper focuses on modeling a disorder ensemble of quantum dots (QDs) as a special kind of Random Geometric Graphs (RGG) with weighted links. We compute any link weight as the overlap integral (or electron probability amplitude) between the QDs (=nodes) involved. This naturally leads to a weighted adjacency matrix, a Laplacian matrix, and a time evolution operator that have meaning in Quantum Mechanics. The model prohibits the existence of long-range links (shortcuts) between distant nodes because the electron cannot tunnel between two QDs that are too far away in the array. The spatial network generated by the proposed model captures inner properties of the QD system, which cannot be deduced from the simple interactions of their isolated components. It predicts the system quantum state, its time evolution, and the emergence of quantum transport when the network becomes connected. View Full-Text
Keywords: quantum dot; disorder array of quantum dots; probability amplitude; complex networks; spatial network; Random Geometric Graphs; quantum transport quantum dot; disorder array of quantum dots; probability amplitude; complex networks; spatial network; Random Geometric Graphs; quantum transport
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MDPI and ACS Style

Cuadra, L.; Nieto-Borge, J.C. Modeling Quantum Dot Systems as Random Geometric Graphs with Probability Amplitude-Based Weighted Links. Nanomaterials 2021, 11, 375. https://doi.org/10.3390/nano11020375

AMA Style

Cuadra L, Nieto-Borge JC. Modeling Quantum Dot Systems as Random Geometric Graphs with Probability Amplitude-Based Weighted Links. Nanomaterials. 2021; 11(2):375. https://doi.org/10.3390/nano11020375

Chicago/Turabian Style

Cuadra, Lucas, and José C. Nieto-Borge. 2021. "Modeling Quantum Dot Systems as Random Geometric Graphs with Probability Amplitude-Based Weighted Links" Nanomaterials 11, no. 2: 375. https://doi.org/10.3390/nano11020375

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