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Arraut, I., Segovia, C., & Rosado, W. (2023). The Hawking Radiation in Massive Gravity: Path Integral and the Bogoliubov Method. Universe, 9(5), 228. https://doi.org/10.3390/universe9050228

We prove the consistency of the different approaches for deriving the black hole radiation for the spherically symmetric case inside the theory of Massive Gravity. By comparing the results obtained by using the Bogoliubov transformations with those obtained by using the Path Integral formulation, we find that in both cases, the presence of the extra-degrees of freedom creates the effect of extra-particles creation due to the distortions on the definitions of time defined by the different observers at large scales. This, however, does not mean extra-particle creation at the horizon level. Instead, the apparent additional particles perceived at large scales emerge from how distant observers define their time coordinate, which is distorted due to the existence of extra-degrees of freedom.

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Arraut, I. (2023). The solution to the Hardy’s paradox (No. arXiv:2106.06397). arXiv. https://doi.org/10.48550/arXiv.2106.06397

By using both, the weak-value formulation as well as the standard probabilistic approach, we analyze the Hardy's experiment introducing a complex and dimensionless parameter ($\epsilon$) which eliminates the assumption of complete annihilation when both, the electron and the positron departing from a common origin, cross the intersection point $P$. We then find that the paradox does not exist for all the possible values taken by the parameter. The apparent paradox only appears when $\epsilon=1$; however, even in this case we can interpret this result as a natural consequence of the fact that the particles can cross the point $P$, but at different times due to a natural consequence of the energy-time uncertainty principle.

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Arraut, I., Marques, J. A. L., Fong, S. J., Li, G., Gois, F. N. B., & Neto, J. X. (2022). A Quantum Field Formulation for a Pandemic Propagation. In J. A. L. Marques & S. J. Fong (Eds.), Epidemic Analytics for Decision Supports in COVID19 Crisis (pp. 141–158). Springer International Publishing. https://doi.org/10.1007/978-3-030-95281-5_6

In this chapter, a mathematical model explaining generically the propagation of a pandemic is proposed, helping in this way to identify the fundamental parameters related to the outbreak in general. Three free parameters for the pandemic are identified, which can be finally reduced to only two independent parameters. The model is inspired in the concept of spontaneous symmetry breaking, used normally in quantum field theory, and it provides the possibility of analyzing the complex data of the pandemic in a compact way. Data from 12 different countries are considered and the results presented. The application of nonlinear quantum physics equations to model epidemiologic time series is an innovative and promising approach.

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Marques, J. A. L., Fong, S. J., Li, G., Arraut, I., Gois, F. N. B., & Neto, J. X. (2022). Research and Technology Development Achievements During the COVID-19 Pandemic—An Overview. In J. A. L. Marques & S. J. Fong (Eds.), Epidemic Analytics for Decision Supports in COVID19 Crisis (pp. 1–15). Springer International Publishing. https://doi.org/10.1007/978-3-030-95281-5_1

At the beginning of 2020, the World Health Organization (WHO) started a coordinated global effort to counterattack the potential exponential spread of the SARS-Cov2 virus, responsible for the coronavirus disease, officially named COVID-19. This comprehensive initiative included a research roadmap published in March 2020, including nine dimensions, from epidemiological research to diagnostic tools and vaccine development. With an unprecedented case, the areas of study related to the pandemic received funds and strong attention from different research communities (universities, government, industry, etc.), resulting in an exponential increase in the number of publications and results achieved in such a small window of time. Outstanding research cooperation projects were implemented during the outbreak, and innovative technologies were developed and improved significantly. Clinical and laboratory processes were improved, while managerial personnel were supported by a countless number of models and computational tools for the decision-making process. This chapter aims to introduce an overview of this favorable scenario and highlight a necessary discussion about ethical issues in research related to the COVID-19 and the challenge of low-quality research, focusing only on the publication of techniques and approaches with limited scientific evidence or even practical application. A legacy of lessons learned from this unique period of human history should influence and guide the scientific and industrial communities for the future.

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Arraut, I., Lobo Marques, J. A., & Gomes, S. (2021). The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance. Mathematics, 9(21), 2777. https://doi.org/10.3390/math9212777

The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets.

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