arXiv subjects

D. Jaramillo

Publications and source records attributed to D. Jaramillo.

3 recordsLinked to original sources

arXiv2012

Classical and Quantum Chaos in the Diamond Shaped Billiard

We analyse the classical and quantum behaviour of a particle trapped in a diamond shaped billiard. We defined this billiard as a half stadium connected with a triangular billiard. A parameter $ξ$ which gradually change the shape of the billiard from a regular equilateral triangle ($ξ=1$) to a diamond ($ξ=0$) was used to control the transition between the regular and chaotic regimes. The classical behaviour is regular when the control parameter $ξ$ is one; in contrast, the system is chaotic when $ξ\neq 1$ even for values of $ξ$ close to one. The entropy grows fast as $ξ$ is decreased from 1 and the Lyapunov exponent remains positive for $ξ<1$. The Finite Difference Method was implemented in order to solve the quantum problem. The energy spectrum and eigenstates were numerically computed for different values of the control parameter. The nearest-neighbour spacing distribution is analysed as a function of $ξ$, finding a Poisson and a Gaussian Orthogonal Ensemble(GOE) distribution for regular and chaotic regimes respectively. Several scars and bouncing ball states are shown with their corresponding classical periodic orbits. Along the document the classical chaos identifiers are computed to show that system is chaotic. On the other hand, the quantum counterpart is in agreement with the Bohigas-Giannoni-Schmit conjecture and exhibits the standard features for chaotic billiard such as the scarring of the wavefunction.

nlin.CD↗

arXiv2003

The Lorentz Group, a Galilean Approach

We present a pedagogical approach to the Lorentz group. We start by introducing a compact notation to express the elements of the fundamental representation of the rotations group.Lorentz coordinate transformations are derived in a novel and compact form. We show how to make a Lorentz transformation on the electromagnetic fields as well. A covariant time-derivative is introduced in order to deal with non-inertial systems. Examples of the usefulness of these results such as the rotating system and the Thomas precession, are also presented

physics.ed-ph↗

arXiv2002

Hierarchical Radiative Quark Mass Matrices with an $U(1)_X$ Horizontal Symmetry Model

In a model with a gauge group $G_{SM}\otimes U(1)_X$, where $G_{SM} \equiv SU(3)_C \otimes SU(2)_L \otimes U(1)_Y$ is the standard model gauge group and $U(1)_X$ is a horizontal local gauge symmetry, we propose a radiative generation of the spectrum of quark masses and mixing angles. The assignment of horizontal charges is such that at tree level only the third family is massive. Using these tree level masses and introducing exotic scalars, the light families of quarks acquire hierarchical masses through radiative corrections. The rank three quark mass matrices obtained are written in terms of a minimal set of free parameters of the model, whose values are estimated performing a numerical fit. The resulting quark masses and CKM mixing angles turn out to be in good agreement with the experimental values.

hep-ph↗