How the inter-electronic potential Ansätze affect the bound state solutions of a planar two-electron quantum dot model

Caruso, Francisco; Oguri, V.; Silveira, Felipe

doi:10.1016/j.physe.2018.09.017

Cited by 11 publications

(5 citation statements)

References 36 publications

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“…The wave functions, obtained in Figure 2, are similar to those found in Ref. [23,30]. They corroborate the conclusion that the topological photon mass plays an important role in system dynamics.…”

Section: Discussion and Final Remarkssupporting

confidence: 87%

Non-relativistic solutions for three-body molecules within a Chern-Simons model

Caruso,

Oguri,

Silveira

et al. 2021

Preprint

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The wave functions and the ground state energies for the bound states of four different muonic and electronic molecules, governed by the Chern-Simons potential in two spatial dimensions, are numerically obtained with the Numerov method. The new results are compared with former planar configuration studies that consider the attractive potential as being proportional to ln(ρ), as well as with the three-dimensional analogs assuming a Coulomb potential.

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Section: Discussion and Final Remarkssupporting

confidence: 87%

Non-relativistic solutions for three-body molecules within a Chern-Simons model

Caruso,

Oguri,

Silveira

et al. 2021

Preprint

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“…We should remember that, over the recent past years, planar physics and truly two-dimensional systems have attracted a great deal of attention in connection with graphene [19][20][21], and with the Quantum Hall Effect [22,23]. All these planar quantum systems point to considering that the correct Coulomb inter-electronic potential should be ln(r) [24], rather than assuming the validity of the usual 3D dependence in planar systems, corresponding to the 1/r potential [25][26][27][28]. This brings us to our general motivation: why should one investigate the 2D μCF.…”

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confidence: 99%

A planar model for the muon-catalyzed fusion

Caruso

Oguri

Silveira

et al. 2019

EPL

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PACS 25.60.Pj -Fusion reactions PACS 25.30.Mr -Muon-induced reactions (including the EMC effect) PACS 36.10.-k -Exotic atoms and molecules (containing mesons, antiprotons and other unusual particles)Abstract -The basic principle of muon catalyzed fusion is that it is possible to obtain energy with temperatures much lower than that required for thermal nuclear fusion. The ground-state energies of muonic molecules formed by ionized proton-proton, deuterium-deuterium and tritium-tritium nuclei plus a negative muon confined in a two-dimensional spatial region are investigated, assuming a ln(r) electrostatic potential instead of the Coulomb potential 1/r frequently used. The effective two-dimensional potential of these molecules is analytically calculated within a quasi-adiabatic approximation, and the probability of fusion is numerically computed for some molecules. In this letter some unexpected theoretical results are given and compared to those of the same molecules described in three dimensions, using the same approach. For example, for the ddμ molecule, the fusion rate is of the order of 10 8 times greater than the predicted value in 3D. For the same molecule, the tunneling rate is also amplified by a factor 10 4 .

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“…Which choice should we made? This question and their implications were discussed in another paper by the authors [20]. Our point of view is that anyway one should expect to have experimental data in order to compare them to the predictions of both models.…”

Section: Discussionmentioning

confidence: 96%

Numerical Solutions for a Two-dimensional Quantum Dot Model

2019

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In this paper, a quantum dot mathematical model based on a twodimensional Schrödinger equation assuming the 1/r inter-electronic potential is revisited. Generally, it is argued that the solutions of this model obtained by solving a biconfluent Heun equation have some limitations. The known polynomial solutions are confronted with new numerical calculations based on the Numerov method. A good qualitative agreement between them emerges. The numerical method being more general gives rise to new solutions. In particular, we are now able to calculate the quantum dot eigenfunctions for a much larger spectrum of external harmonic frequencies as compared to previous results. Also the existence of bound state for such planar system, in the case = 0, is predicted and its respective eigenvalue is determined. Keywords Quantum dot model · Numerov numerical method · two-electron system · Schrödinger equation PACS PACS 81.07.Ta · 78.67.Hc · 36.10.-k 1 IntroductionModern technics in nanometer-scale semiconductor manufacturing enable the creation of quantum confinement of only a few electrons. These few-body systems are often called quantum dots [1]. They can be described by a model F. Caruso

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How the inter-electronic potential Ansätze affect the bound state solutions of a planar two-electron quantum dot model

Cited by 11 publications

References 36 publications

Non-relativistic solutions for three-body molecules within a Chern-Simons model

Non-relativistic solutions for three-body molecules within a Chern-Simons model

A planar model for the muon-catalyzed fusion

Numerical Solutions for a Two-dimensional Quantum Dot Model

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