Francisco Caruso | Centro Brasileiro de Pesquisas Físicas (original) (raw)
Papers by Francisco Caruso
Cosmos & Contexto, 2024
Aqui se conta uma história de alguns segredos, tão antigos quanto algo entre 240 e 350 mil anos, ... more Aqui se conta uma história de alguns segredos, tão antigos quanto algo entre 240 e 350 mil anos, revelados por uma misteriosa caverna. É uma história que ganha vida como um palimpsesto, sobrepondo-se à outra, narrada no documentário Caverna de Ossos, da série Explorando o Desconhecido. Impossível não ficar impactado por esse relato, pois levanta várias questões intrigantes sobre a evolução humana e sobre a própria definição de humano. Essa narrativa, mais do que pela razão formal e analítica, é conduzida pela poética do tempo arcaico, ou seja, é levada pela emoção de vislumbrar raízes da natureza humana, tão distantes-pré-históricas-e pelo fascínio de muitas das indagações interdisciplinares postas aqui em evidência. É, em última análise, uma breve história de devaneio acerca do significado de ser humano.
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Revista Brasileira de Ensino de Física , 2024
Partindo da perspectiva de reportagens publicadas em jornais brasileiros da época, bem como de ca... more Partindo da perspectiva de reportagens publicadas em jornais brasileiros da época, bem como de cartas trocadas entre cientistas que trabalhavam no Brasil e colegas norte-americanos, e documentos do simpósio sobre raios cósmicos, traça-se uma sequência cronológica de como ocorreu a chamada missão Compton no Brasil e como foi percebida pelo público alfabetizado. Para uma melhor compreensão do artigo, contextualizam-se as pesquisas em raios cósmicos no Brasil e no mundo e discutem-se os motivos da criação da missão e de sua vinda para o Brasil.
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Vitruvian Cogitationes, May 16, 2022
Dois períodos ímpares na História, nos quais houve grande aproximação e intersecção entre Arte e ... more Dois períodos ímpares na História, nos quais houve grande aproximação e intersecção entre Arte e Ciência, são apresentados e analisados. Em particular, foca-se em suas origens e seus impactos sobre os fazeres, os saberes e sobre o Homem.
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arXiv (Cornell University), Mar 28, 2022
Neste trabalho, apresenta-se uma tentativa (incompleta) de compreen- der a contribuição de Gali... more Neste trabalho, apresenta-se uma tentativa (incompleta) de compreen-
der a contribuição de Galileu Galilei no âmbito da História das Ideias, a partir
do momento em que aponta uma luneta para o céu. Para isso, foi preciso, antes,
que Giotto pintasse o céu de azul. Reconstruímos toda essa fascinante trajetória
entre os séculos XIII e XVII na Europa, relacionando diferentes fazeres e saberes,
bem como discutindo o pensamento científico e filosófico daquela época. A
tese principal desse ensaio é mostrar que Giotto, quem pintou o céu de azul
numa cultura que o desejava dourado, percorreu uma trajetória conceitual muito
semelhante àquela trilhada por Galileu séculos depois.
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Jornal Mato-Grossense de Física , 2023
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Ciência e Cultura, Dec 1, 2005
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Ciência e Sociedade, Apr 1, 2019
Faz-se um breve apanhado da contribuição científica de José Leite Lopes, procurando relacioná-la ... more Faz-se um breve apanhado da contribuição científica de José Leite Lopes, procurando relacioná-la com suas atividades como educador, como defensor intransigente do desenvolvimento nacional e latino-americano da Física, e como criador e estimulador de um ambiente propício para o fazer científico no Brasil.
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Caderno Brasileiro de Ensino de Física, Aug 24, 2009
Faz-se um breve apanhado do impacto da contribuição de Einstein referente aos seguintes conceitos... more Faz-se um breve apanhado do impacto da contribuição de Einstein referente aos seguintes conceitos: espaço, tempo, simultaneidade, massa e energia. Apresentam-se alguns objetivos relacionados a um projeto de educação através de histórias em quadrinhos, no qual este trabalho se insere, e um conjunto de sete tirinhas originais, que pode ser utilizado pelos professores de Ensino Médio como suporte para uma abordagem lúdica e divertida da Física Moderna, evidenciando as contribuições de Einstein para a consolidação da importante revolução científica que foi a sua Teoria da Relatividade.
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Ciência e Sociedade, Jun 1, 2014
O artigo resume a ideia central do texto lido pelo autor na cerimônia de sua posse na Academia Br... more O artigo resume a ideia central do texto lido pelo autor na cerimônia de sua posse na Academia Brasileira de Filosofia, em 28 de novembro de 2013, com o qual se faz um convite à reflexão sobre os caminhos que a Educação, e em especial a Escola, vêm trilhando em nosso país.
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Giornale di Fisica , 1986
It is shown that there is a simple way to get the quantization equation for the electric and magn... more It is shown that there is a simple way to get the quantization equation for the electric and magnetic charges of dyons, e_i g_j − g_i e_j = m (ℏc), which also shed light to the origin of such quantization.
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International Journal of Modern Physics A, May 20, 1999
The renormalized energy density of a massless scalar field defined in a D-dimensional flat space–... more The renormalized energy density of a massless scalar field defined in a D-dimensional flat space–time is computed in the presence of "soft" and "semihard" boundaries, modeled by some smoothly increasing potential functions. The sign of the renormalized energy densities for these different confining situations is investigated. The dependence of this energy on D for the cases of "hard" and "soft/semihard" boundaries are compared.
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Physical Review D , 1991
The dependence of Casimir energy (associated with a massless scalar field) on spacetime dimension... more The dependence of Casimir energy (associated with a massless scalar field) on spacetime dimensionality (𝐷) is shown to be strongly entangled with the type of geometric bounds and the kind of macroscopic boundary conditions imposed on the field. In the case of a massless scalar field satisfying Dirichlet boundary conditions in the presence of a hyperparallelepipedal cavity with 𝑝 sides of finite length 𝐿 and 𝐷−𝑝−1 sides with length much greater than 𝐿, a new compact integral formula, more suitable to analyze the nature of the Casimir force, is obtained. The force is attractive if 𝑝 is odd or for very large even values of 𝑝, irrespective of 𝐷. For each small even 𝑝 there exists a critical spacetime dimension 𝐷𝑐(𝑝) such that the force is repulsive if 𝐷<𝐷𝑐 and attractive otherwise. As a consequence, the instability of the semiclassical Abraham-Lorentz-Casimir model of the electron is proved to depend on the spacetime dimensionality.
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Cosmos & Contexto, 2024
Aqui se conta uma história de alguns segredos, tão antigos quanto algo entre 240 e 350 mil anos, ... more Aqui se conta uma história de alguns segredos, tão antigos quanto algo entre 240 e 350 mil anos, revelados por uma misteriosa caverna. É uma história que ganha vida como um palimpsesto, sobrepondo-se à outra, narrada no documentário Caverna de Ossos, da série Explorando o Desconhecido. Impossível não ficar impactado por esse relato, pois levanta várias questões intrigantes sobre a evolução humana e sobre a própria definição de humano. Essa narrativa, mais do que pela razão formal e analítica, é conduzida pela poética do tempo arcaico, ou seja, é levada pela emoção de vislumbrar raízes da natureza humana, tão distantes-pré-históricas-e pelo fascínio de muitas das indagações interdisciplinares postas aqui em evidência. É, em última análise, uma breve história de devaneio acerca do significado de ser humano.
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Revista Brasileira de Ensino de Física , 2024
Partindo da perspectiva de reportagens publicadas em jornais brasileiros da época, bem como de ca... more Partindo da perspectiva de reportagens publicadas em jornais brasileiros da época, bem como de cartas trocadas entre cientistas que trabalhavam no Brasil e colegas norte-americanos, e documentos do simpósio sobre raios cósmicos, traça-se uma sequência cronológica de como ocorreu a chamada missão Compton no Brasil e como foi percebida pelo público alfabetizado. Para uma melhor compreensão do artigo, contextualizam-se as pesquisas em raios cósmicos no Brasil e no mundo e discutem-se os motivos da criação da missão e de sua vinda para o Brasil.
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Vitruvian Cogitationes, May 16, 2022
Dois períodos ímpares na História, nos quais houve grande aproximação e intersecção entre Arte e ... more Dois períodos ímpares na História, nos quais houve grande aproximação e intersecção entre Arte e Ciência, são apresentados e analisados. Em particular, foca-se em suas origens e seus impactos sobre os fazeres, os saberes e sobre o Homem.
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arXiv (Cornell University), Mar 28, 2022
Neste trabalho, apresenta-se uma tentativa (incompleta) de compreen- der a contribuição de Gali... more Neste trabalho, apresenta-se uma tentativa (incompleta) de compreen-
der a contribuição de Galileu Galilei no âmbito da História das Ideias, a partir
do momento em que aponta uma luneta para o céu. Para isso, foi preciso, antes,
que Giotto pintasse o céu de azul. Reconstruímos toda essa fascinante trajetória
entre os séculos XIII e XVII na Europa, relacionando diferentes fazeres e saberes,
bem como discutindo o pensamento científico e filosófico daquela época. A
tese principal desse ensaio é mostrar que Giotto, quem pintou o céu de azul
numa cultura que o desejava dourado, percorreu uma trajetória conceitual muito
semelhante àquela trilhada por Galileu séculos depois.
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Jornal Mato-Grossense de Física , 2023
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Ciência e Cultura, Dec 1, 2005
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Ciência e Sociedade, Apr 1, 2019
Faz-se um breve apanhado da contribuição científica de José Leite Lopes, procurando relacioná-la ... more Faz-se um breve apanhado da contribuição científica de José Leite Lopes, procurando relacioná-la com suas atividades como educador, como defensor intransigente do desenvolvimento nacional e latino-americano da Física, e como criador e estimulador de um ambiente propício para o fazer científico no Brasil.
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Caderno Brasileiro de Ensino de Física, Aug 24, 2009
Faz-se um breve apanhado do impacto da contribuição de Einstein referente aos seguintes conceitos... more Faz-se um breve apanhado do impacto da contribuição de Einstein referente aos seguintes conceitos: espaço, tempo, simultaneidade, massa e energia. Apresentam-se alguns objetivos relacionados a um projeto de educação através de histórias em quadrinhos, no qual este trabalho se insere, e um conjunto de sete tirinhas originais, que pode ser utilizado pelos professores de Ensino Médio como suporte para uma abordagem lúdica e divertida da Física Moderna, evidenciando as contribuições de Einstein para a consolidação da importante revolução científica que foi a sua Teoria da Relatividade.
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Ciência e Sociedade, Jun 1, 2014
O artigo resume a ideia central do texto lido pelo autor na cerimônia de sua posse na Academia Br... more O artigo resume a ideia central do texto lido pelo autor na cerimônia de sua posse na Academia Brasileira de Filosofia, em 28 de novembro de 2013, com o qual se faz um convite à reflexão sobre os caminhos que a Educação, e em especial a Escola, vêm trilhando em nosso país.
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Giornale di Fisica , 1986
It is shown that there is a simple way to get the quantization equation for the electric and magn... more It is shown that there is a simple way to get the quantization equation for the electric and magnetic charges of dyons, e_i g_j − g_i e_j = m (ℏc), which also shed light to the origin of such quantization.
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International Journal of Modern Physics A, May 20, 1999
The renormalized energy density of a massless scalar field defined in a D-dimensional flat space–... more The renormalized energy density of a massless scalar field defined in a D-dimensional flat space–time is computed in the presence of "soft" and "semihard" boundaries, modeled by some smoothly increasing potential functions. The sign of the renormalized energy densities for these different confining situations is investigated. The dependence of this energy on D for the cases of "hard" and "soft/semihard" boundaries are compared.
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Physical Review D , 1991
The dependence of Casimir energy (associated with a massless scalar field) on spacetime dimension... more The dependence of Casimir energy (associated with a massless scalar field) on spacetime dimensionality (𝐷) is shown to be strongly entangled with the type of geometric bounds and the kind of macroscopic boundary conditions imposed on the field. In the case of a massless scalar field satisfying Dirichlet boundary conditions in the presence of a hyperparallelepipedal cavity with 𝑝 sides of finite length 𝐿 and 𝐷−𝑝−1 sides with length much greater than 𝐿, a new compact integral formula, more suitable to analyze the nature of the Casimir force, is obtained. The force is attractive if 𝑝 is odd or for very large even values of 𝑝, irrespective of 𝐷. For each small even 𝑝 there exists a critical spacetime dimension 𝐷𝑐(𝑝) such that the force is repulsive if 𝐷<𝐷𝑐 and attractive otherwise. As a consequence, the instability of the semiclassical Abraham-Lorentz-Casimir model of the electron is proved to depend on the spacetime dimensionality.
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Science, 2005
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Contemporary Physics, 2018
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Contemporary Physics, 2013
‘dark’) members of the system. The reality turned out to be much richer than that. The term ‘dark... more ‘dark’) members of the system. The reality turned out to be much richer than that. The term ‘dark matter’ is used literally to mean very-low luminosity objects and, as well as the expected non-baryonic dark matter, there is significant discussion of ‘stars of poor visibility’, compact objects (white dwarfs, neutron stars and black holes), neutrinos, comets, asteroids and extra-solar planets. In addition, there is a wealth of preparatory material covering topics as diverse as co-ordinate systems, cosmological models, early particle physics experimentation, particle physics, radioactive decay, symmetry laws and neutrino physics. The book is arranged in nine chapters plus an epilogue. Although there is some logic to the arrangement and content, it is sometimes not apparent at first sight. In the preface, we get a clue as to why this is the case when the author writes ‘Due to my on-and-off writing style and a continuous outpouring of cosmic events that required reporting, the project has been delayed much too much.’ The author has attempted to be all embracing in terms of her interests and parts of the book look to have grown organically with the inevitable race to keep up with everything. In the last respect, it should be noted that there is very little that goes beyond 2001 in any of the topics, which is a major disappointment in a book published in 2012. It is, however, understandable given the breadth of the task the author set herself and the sheer scale of the significant advances that have been made in almost every aspect of the subject matter. However, the book is still well worth a read, giving an in-depth insight into the status of ‘dark matter’ research in those early years. In the foreword (by Marvin Minsky), we find the following ‘While much of the text is for the math-loving scientists, other readers can just skip these technical parts ...’. There are indeed a number of sections with significant chunks of equation after equation. This reflects the author’s background in mathematics. At times it can be difficult to understand what message or conclusion the author is intending the reader to take from those sections as there is very little supporting summary text in those parts. In fact, even the more descriptive chapters often lack a ‘summary’ and the reader can be left just with a feeling that they have read a lot of interesting facts but are not getting the ‘big picture’. Each chapter comes with complete references and ‘comments’ which are information snippets relevant to the chapter but not woven into it. The Epilogue is a collection of 19 ‘latest news’ offerings and is rather limited. Finally, a comment on the myriad of issues which have hopefully been picked up in proof reading as the copy-reviewed was a ‘Galley Proof’. As an example, some figures had the wrong images, some figures were missing and some grey-scale figures had colours referred to in their captions. If thinking of buying a copy, a recommended quick check would be to compare Figures 1.2 and 1.5, as in the review copy they have the same image. References were quite extensive but not always presented to the same standard or format. Some equations did have errors.
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Contemporary Physics, 2020
I was introduced to the concept of ether (or aether) as an undergraduate student in Physics. From... more I was introduced to the concept of ether (or aether) as an undergraduate student in Physics. From the first moment, it seemed to me a very unique and strange concept in the History of Physics: A co...
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Contemporary Physics, Jun 27, 2018
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Contemporary Physics, 2020
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Contemporary Physics, Oct 2, 2018
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Contemporary Physics, Oct 2, 2019
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Contemporary Physics, Nov 1, 2013
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Caderno Brasileiro de Ensino de Física, 2005
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Contemporary Physics
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Book review
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Contemporary Physics, 2018
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Norte Ciência, 2011
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Norte Ciência, 2011
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Ciência Hoje, 1997
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Dialoghi: Rivista di Studi Italici, 2001
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A Física na Escola, 2005
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CBPF Thesis, 1983
We critically review the present status of glueballs, including theoretical and experimental aspe... more We critically review the present status of glueballs, including theoretical and experimental aspects.
We present a set of favored processes where it may be possible to search for these objects. We stress some of the existent problems related to the unambiguous prediction of their properties.
We propose a model which is able to explain the experimental data for the reaction pi−prightarrowphiphin\pi^- p \rightarrow \phi\phi npi−prightarrowphiphin, allowing us to estimate the coupling constants gGphiphig_{G\phi\phi}gGphiphi e gGpipig_{G\pi\pi}gGpipi of a 2++2^{++}2++ glueball state to phiphi\phi\phiphiphi e pipi\pi\pipipi, respectively.
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PhD Thesis Università di Torino, 1989
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Dialoghi: Rivista di Studi Italici, 1998
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Resumo: Procura-se identificar algumas das origens históricas do negacionismo, dando ênfase aos s... more Resumo: Procura-se identificar algumas das origens históricas do negacionismo, dando ênfase aos seus aspectos filosóficos. Apresenta-se uma revisão de alguns conceitos basilares como os de verdade e episteme, destacando o quanto foram importantes na História das Ideias e na Filosofia Ocidental. Analisa-se, ainda que de forma resumida, o aspecto social da questão, por meio da compreensão da mudança do sujeito e suas relações de trabalho ao longo da História, principalmente no período pós-industrial. Por fim, discute-se a práxis negacionista, destacando suas principais influências filosóficas e consequências.
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Caçador de Estrelas: Homenagem a Rubens de Azevedo, 2022
Neste trabalho, apresenta-se uma tentativa (incompleta) de compreender a contribuição de Galileu ... more Neste trabalho, apresenta-se uma tentativa (incompleta) de compreender a contribuição de Galileu no âmbito da História das Ideias, relacionando-a com outros fazeres e saberes, bem como o pensamento científico e filosófico daquela época.
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Resumo: Dois períodos ímpares na História, nos quais houve grande aproximação e intersecção en-tr... more Resumo: Dois períodos ímpares na História, nos quais houve grande aproximação e intersecção en-tre Arte e Ciência, são apresentados e analisados. Em particular, foca-se em suas origens e seus impactos sobre os fazeres, os saberes e sobre o Homem.
Abstract: Two unique periods in History, in which there was a great approximation and intersection between Art and Science, are presented and analyzed. Specifically, it focuses on its origins and its impacts on practices, knowledge and on man.
Resumen: Se presentan y analizan dos períodos únicos en la historia, en los que hubo una gran aproxi-mación e intersección entre Arte y Ciencia. En particular, se centra en sus orígenes y sus impactos en las prácticas, el conocimiento y el hombre.
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arXiv:2009.13473v1, 2020
Hydrogen atom is supposed to be described by a generalization of Schrödinger equation , in which ... more Hydrogen atom is supposed to be described by a generalization of Schrödinger equation , in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential r −β. Starting from previously obtained solutions for this equation using the 1/N expansion method, it is shown that new light can be shed on the problem of understanding the dimensionality of the world as proposed by Paul Ehrenfest. A surprisingly new result is obtained. Indeed, for the first time, we can understand that not only the sign of energy but also the value of the ground state energy of hydrogen atom is related to the threefold nature of space. How do the fundamental laws of Physics and space-time dimensionality are entangled? The genesis of this kind of investigation can be traced back to the doctoral thesis of Immanuel Kant [1]. The role played by space dimensionality in determining the form of various physical laws and constants of nature was reviewed in Ref. [2]. A systematic scientific investigation of this general question begins with the semi-nal contributions of Paul Ehrenfest [3, 4]. His general idea was to identify particular aspects of a physical system or phenomenon, called by him "singular aspects", which could be used to distinguish the Physics in three-dimensional space from that in D-dimensions. To carry on this project, he started from postulating that the form of a differential equation-which usually describes a physical phenomenon in a three-dimensional space-is still valid for an arbitrary number of dimensions. As an example, Ehrenfest assumed the motion of a planet under a central force associated with the Newtonian gravitational potential to be still described by the Laplace-Poisson equation , keeping the same power of the Laplacian operator ∆ and making the number of coordinates change from 3 to D. Based on the general mathematical solution of such equation, he imposed that they should satisfy the postulate of the stability of orbital motion under central forces to get at the proper number of dimensions. It is clear that, in this case, one cannot claim to have demonstrated that D = 3 for an obvious reason: The Poisson equation for the Newtonian potential is, by construction, an equation that effectively describes stable orbits in 3-dimensions [5]. Thus, Ehrenfest's result was already expected and, actually, it has to be seen almost as a consistency check of the theoretical description of stable planetary motion. Using a semi-classical approach, Ehrenfest, based on Niels Bohr quantization of circular atomic orbits generated by a Coulomb-like potential-formally analogous to 1
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arXiv:2009.03894 [quant-ph], 2020
Bidimensional muonic and electronic atoms, with nuclei composed of a proton, deuteron, and triton... more Bidimensional muonic and electronic atoms, with nuclei composed of a proton, deuteron, and triton, and governed by Chern-Simons potential, are numerically solved. Their eigenvalues and eigenfunctions are determined with a slightly modified Numerov method. Results are compared with those assuming that the same atoms are governed by the usual 1/r potential even in a two-dimensional space, as well as with its three-dimensional analogs.
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arXiv:2009.13473 [quant-ph], 2020
Hydrogen atom is supposed to be described by a generalization of Schrödinger equation , in which ... more Hydrogen atom is supposed to be described by a generalization of Schrödinger equation , in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential r −β. Starting from previously obtained solutions for this equation using the 1/N expansion method, it is shown that new light can be shed on the problem of understanding the dimensionality of the world as proposed by Paul Ehrenfest. A surprisingly new result is obtained. Indeed, for the first time, we can understand that not only the sign of energy but also the value of the ground state energy of hydrogen atom is related to the threefold nature of space. How do the fundamental laws of Physics and space-time dimensionality are entangled? The genesis of this kind of investigation can be traced back to the doctoral thesis of Immanuel Kant [1]. The role played by space dimensionality in determining the form of various physical laws and constants of nature was reviewed in Ref. [2]. A systematic scientific investigation of this general question begins with the semi-nal contributions of Paul Ehrenfest [3, 4]. His general idea was to identify particular aspects of a physical system or phenomenon, called by him "singular aspects", which could be used to distinguish the Physics in three-dimensional space from that in D-dimensions. To carry on this project, he started from postulating that the form of a differential equation-which usually describes a physical phenomenon in a three-dimensional space-is still valid for an arbitrary number of dimensions. As an example, Ehrenfest assumed the motion of a planet under a central force associated with the Newtonian gravitational potential to be still described by the Laplace-Poisson equation , keeping the same power of the Laplacian operator ∆ and making the number of coordinates change from 3 to D. Based on the general mathematical solution of such equation, he imposed that they should satisfy the postulate of the stability of orbital motion under central forces to get at the proper number of dimensions. It is clear that, in this case, one cannot claim to have demonstrated that D = 3 for an obvious reason: The Poisson equation for the Newtonian potential is, by construction, an equation that effectively describes stable orbits in 3-dimensions [5]. Thus, Ehrenfest's result was already expected and, actually, it has to be seen almost as a consistency check of the theoretical description of stable planetary motion. Using a semi-classical approach, Ehrenfest, based on Niels Bohr quantization of circular atomic orbits generated by a Coulomb-like potential-formally analogous to 1
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The basic principle of muon catalyzed fusion is that is possible to obtain energy with temperatur... more The basic principle of muon catalyzed fusion is that is possible to obtain energy with temperatures much lower than the 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 is investigated, assuming a ln(r)\ln(r)ln(r) electrostatic potential instead of the Coulomb potential 1/r1/r1/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 ddmudd\muddmu molecule, the fusion rate is of the order of 10810^8108 times greater than the predicted value in 3D. For the same molecule, the tunneling rate is also amplified by a factor simeq104\simeq 10^4simeq104.
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CBPF-NF-004/19, 2019
The ground state energy, its respective eigenfunction and some specific parameters of ionized muo... more The ground state energy, its respective eigenfunction and some specific parameters of ionized muonic molecules formed by proton-proton, deuterium-deuterium and tritium-tritium nuclei plus a negative muon confined in a two-dimensional spatial region are calculated. A 2D Coulombic potential of the type ln(r)\ln (r)ln(r) is considered for the electrostatic interaction, instead of the usual 3D 1/r1/r1/r potential. The two-dimensional effective potentials of these three-body molecules are analytically calculated within a quasi-adiabatic approximation. Then, the resulting Schrö\-din\-ger equation is numerically solved for each kind of molecule with a slightly modified Numerov method. The results are confronted with those got for the same molecules in 3D and 2D, in both cases adopting the 1/r1/r1/r Ansatz. On the one hand, these comparisons put in evidence that the choice of the potential energy significantly influences the nuclear fusion probability. In particular, we find, for the ttmutt\muttmu molecule, that this probability is 10910^9109 times greater using the two-dimensional ln(r)\ln(r)ln(r) Coulombic potential compared to the prediction in three-dimensions with the 1/r1/r1/r potential. In addition, for this same molecule, the tunnelling ratio is 2times1042 \times 10^{4}2times104 greater than in 3D. On the other hand, all these results put in evidence also the distinguished role of the ``centrifugal potential'' in the 2D effective potential, showing that the geometrical nature of planar space plays a quite relevant role for the improvement of fusion rates in 2D.
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Apresentam-se argumentos em favor da inclusão da História e Filosofia da Ciência nos cursos de Gr... more Apresentam-se argumentos em favor da inclusão da História e Filosofia da Ciência nos cursos de Graduação (Bacharelado e Licenciatura) em Física.
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