arXiv subjects
Publications and source records attributed to J. C. Castro-Palacio.
The cosmological constant and the Boltzmann entropy of a Newtonian Universe filled with a perfect fluid are computed, under the assumption that spatial sections are copies of 3-dimensional hyperbolic space.
We compute the cosmological constant of a spherical space in the limit of weak gravity. To this end we use a duality developed by the present authors in a previous work. This duality allows one to treat the Newtonian cosmological fluid as the probability fluid of a single particle in nonrelativistic quantum mechanics. We apply this duality to the case when the spacetime manifold on which this quantum mechanics is defined is given by $\mathbb{R}\times\mathbb{S}^3$. Here $\mathbb{R}$ stands for the time axis and $\mathbb{S}^3$ is a 3-dimensional sphere endowed with the standard round metric. A quantum operator $Λ$ satisfying all the requirements of a cosmological constant is identified, and the matrix representing $Λ$ within the Hilbert space $L^2\left(\mathbb{S}^3\right)$ of quantum states is obtained. Numerical values for the expectation value of the operator $Λ$ in certain quantum states are obtained, that are in good agreement with the experimentally measured cosmological constant.
The reaction times of individuals over consecutive visual stimuli have been studied using spectral analysis and a failure machinery approach. The used tools include the fast Fourier transform and a spectral entropy analysis. The results indicate that the reaction times produced by the independently responding individuals to visual stimuli appear to be correlated. The spectral analysis and the entropy of the spectrum yield that there are features of similarity in the response times of each participant and among them. Furthermore, the analysis of the mistakes made by the participants during the reaction time experiments concluded that they follow a behavior which is consistent with the MTBF (Mean Time Between Failures) model, widely used in industry for the predictive diagnosis of electrical machines and equipment.
We present a simple quantum-mechanical estimate of the cosmological constant of a Newtonian Universe. We first mimic the dynamics of a Newtonian spacetime by means of a nonrelativistic quantum mechanics for the matter contents of the Universe (baryonic and dark) within a fixed (i.e., nondynamical) Euclidean spacetime. Then we identify an operator that plays, on the matter states, a role analogous to that played by the cosmological constant. Finally we prove that there exists a quantum state for the matter fields, in which the above mentioned operator has an expectation value equal to the cosmological constant of the given Newtonian Universe.
In this work, we analyzed time-series of background radiation inside a multilayer interleaving structure, geomagnetic activity and cosmic-ray activity using the Pearson correlation coefficient and a new correlation measure based on the one-dimensional component of the fourth order cumulant. The new method is proposed based on the fact that the cumulant of a random process is zero if it is of Gaussian nature. The results show that this methodology is useful for detecting correlations between the analyzed variables.
Velazquez and Curilef have proposed a methodology to extend Monte Carlo algorithms that are based on canonical ensemble. According to our previous study, their proposal allows us to overcome slow sampling problems in systems that undergo any type of temperature-driven phase transition. After a comprehensive review about ideas and connections of this framework, we discuss the application a re-weighting technique to improve the accuracy of microcanonical calculations, specifically, the well-known multi-histograms method of Ferrenberg and Swendsen. As example of application, we reconsider the study of four-state Potts model on the square lattice $L\times L$ with periodic boundary conditions. This analysis allows us to detect the existence of a very small latent heat per site $q_{L}$ during the occurrence of temperature-driven phase transition of this model, whose size dependence seems to follow a power-law $q_{L}(L)\propto(1/L)^{z}$ with exponent $z\simeq0$.$26\pm0$.$02$. It is discussed the compatibility of these results with the continuous character of temperature-driven phase transition when $L\rightarrow+\infty$.
Recently, Velazquez and Curilef have proposed a methodology to extend Monte Carlo algorithms based on canonical ensemble, which is aimed to overcome slow sampling problems associated with temperature-driven discontinuous phase transitions. We show in this work that Monte Carlo algorithms extended with this methodology also exhibit a remarkable efficiency near a critical point. Our study is performed for the particular case of 2D four-state Potts model on the square lattice with periodic boundary conditions. This analysis reveals that the extended version of Metropolis importance sample is more efficient than the usual Swendsen-Wang and Wolff cluster algorithms. These results demonstrate the effectiveness of this methodology to improve the efficiency of MC simulations of systems that undergo any type of temperature-driven phase transition.