arXiv subjects

R. O. Francisco

Publications and source records attributed to R. O. Francisco.

5 recordsLinked to original sources

arXiv2024

Generalized Uncertainty Principle for Entangled States of Two Identical Particles

In this work we determine the consequences of the quantum entanglement of a system of two identical particles when a generalized uncertainty principle (GUP) is considered. GUP's are usually associated with the existence of a minimal length. We focus on the main GUP's (KMM, ADV, Pedram and Nouicer) and then we determine the minimal uncertainties in position induced by those modified GUP's. Our results point out that the minimal uncertainty is reduced by half of its usual value independently of the GUP employed. This implies that the minimal length is also reduced by half. On the other hand, it is generally expected that the minimal length must not depend on physical system. We overcome this apparent paradox by realizing that the entangled system is composed by two particles so that an effective parameter related to the minimal length must be employed.

quant-ph↗

arXiv2018

Dirac $δ$-function potential in quasiposition representation of a minimal-length scenario

A minimal-length scenario can be considered as an effective description of quantum gravity effects. In quantum mechanics the introduction of a minimal length can be accomplished through a generalization of Heisenberg's uncertainty principle. In this scenario, state eigenvectors of the position operator are no longer physical states and the representation in momentum space or a representation in a quasiposition space must be used. In this work, we solve the Schroedinger equation with Dirac $δ$-function potential in quasiposition space. We calculate the bound state energy and the coefficients of reflection and transmission for scattering states. We show that leading corrections are of order of the minimal length $({\sl O}(\sqrtβ))$ and the coefficients of reflection and transmission are no longer the same for the Dirac delta well and barrier as in ordinary quantum mechanics. Furthermore, assuming that the equivalence of the 1s state energy of the hydrogen atom and the bound state energy of the Dirac $δ$-function potential in 1-dim is kept in a minimal-length scenario, we also find that the leading correction term for the ground state energy of the hydrogen atom is of order of the minimal length and $Δx_{min} \le 10^{-25}$ m.

hep-th↗

arXiv2014

Relativistic Approach to the Hydrogen Atom in a Minimal Length Scenario

In this work we show that relativistic contributions to the ground state energy of the hydrogen atom arising from the presence of a minimal length introduced by a Lorentz-covariant algebra are more relevant than non-relativistic ones, and because of this the non-relativistic approach is not suitable. In addition, comparing our result with experimental data we can roughly estimate the upper bound for the minimal length value of the order $10^{-20}m$.

hep-th↗

arXiv2013

Ground State of the Hydrogen Atom via Dirac Equation in a Minimal Length Scenario

In this work we calculate the correction to the ground state energy of the hydrogen atom due to contributions arising from the presence of a minimal length. The minimal length scenario is introduced by means of modifying the Dirac equation through a deformed Heisenberg algebra (kempf algebra). With the introduction of the Coulomb potential in the new Dirac energy operator, we calculate the energy shift of the ground state of the hydrogen atom in first order of the parameter related to the minimal length via perturbation theory.

hep-th↗

arXiv2012

Neumann boundary conditions inhibiting the SSB in the Coleman-Weinberg mechanism

In this work we show that homogeneous Neumann boundary conditions inhibit the Coleman-Weinberg mechanism for spontaneous symmetry breaking in the scalar electrodynamics if the length of the finite region is small enough ($a = e^{2}M^{-1}_ϕ$, where $M_ϕ$ is the mass of the scalar field generated by the Coleman-Weinberg mechanism)

hep-th↗