V. Oguri

The Cosmic Microwave Background Spectrum and an Upper Limit for Fractal Space Dimensionality

The possibility of constraining fractal space dimensionality from astrophysics and other areas is briefly reviewed. Assuming such dimensionality to be 3 + , a bound for can be imposed from data obtained by far-infrared absolute spectrophotometer instrument aboard Cosmic Background Explorer satellite. The available data for the cosmic microwave background radiation (CMBR) spectrum are fitted by Plancks radiation distribution generalized to noninteger space dimensionality. The present analysis shows that the shape of the CMBR spectrum, which does not depend on the absolute normalization, is correctly described from this distribution provided the absolute temperature is equal to (2.726 ± 0.003) × 10–2 K and = –(0.957 ± 0.006) × 10–5. This result for the last parameter is shown to be similar to what was found on a very different spatial scale based on a quantum phenomenon. The value of || is interpreted as an upper limit for how much space dimensionality could have deviated from three. In other words, this is the maximum fluctuation space dimensionality should have undertaken in a very large spatial and temporal scale compared to that of the decoupling era.

Solving a two-electron quantum dot model in terms of polynomial solutions of a Biconfluent Heun equation

Abstract The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are investigated. In particular, it is shown that it is possible to determine exactly and in a closed form a finite portion of the energy spectrum and the associated eigenfunctions for the Schrodinger equation describing the relative motion of the electrons, by putting it into the form of a biconfluent Heun equation. In the same framework, another set of solutions of this type can be straightforwardly obtained for the case when the two electrons are submitted also to an external constant magnetic field.

On the existence of hydrogen atoms in higher dimensional Euclidean spaces

Abstract The question of whether hydrogen atoms can exist or not in spaces with a number of dimensions ( D ) greater than 3 is revisited. The lowest quantum mechanical stable states and the corresponding wave functions are determined by applying Numerovʼs method to solve Schrodingerʼs equation. States for different angular momentum quantum number and dimensionality are considered. One is lead to the result that hydrogen atoms in higher dimensions could actually exist. The most probable distance between the electron and the nucleus are then computed as a function of D showing the possibility of tiny confined states.

A Eterna Busca do Indivisível: do Átomo Filosófico aos Quarks e Léptons

The fascinating search of the inner boundaries of the Universe, has been entangled, since the birth of greek philosophy 25 centuries ago, with the main epistemological changes in the History of Science. This paper does not intend to present a systematic description of the discovery of the elementary particles. By stressing the main achievements of the knowledge of matters structure and their dependence on symmetry arguments, it is argued that even considering profound differences in each historical period, there is a paradgima of atom shared by Chemistry and Particle Physics. This text could help High School Teachers of Chemistry and Physics, as well as motivate them, in the challenge of explaining to their pupils how the idea of atom evolved.

Fixing two chiral perturbation theory parameters by fitting pion pion phase shifts

Abstract In this paper, we fix the parameters l 1 and l 2 of the one loop corrected chiral perturbation theory by fitting the low energy pion-pion S- and P- experimental phase-shifts. The corresponding values of the scattering lengths are calculated. Related approaches for data fitting, in particular the unitarization program of current algebra, are also discussed.

Does Dirac equation for a generalized Coulomb-like potential in D+1 dimensional flat space–time admit any solution for D≥4 ?

The relativistic hydrogen atom in an Euclidean space-time of arbitrary number of space dimensions (

Effects on the non-relativistic dynamics of a charged particle interacting with a Chern-Simons potential

D

Kaon-pion low energy phase shifts from chiral perturbation theory

) plus one time dimension is revisited. In particular, numerical solutions of the radial Dirac equation for a generalized Coulombian potential proportional to

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

1/r^{(D-2)}

Specific heats of degenerate ideal gases

are investigated. It is argued that one could not find any physical solution for