arXiv subjects

G. Báez

Publications and source records attributed to G. Báez.

12 recordsLinked to original sources

arXiv2024

The rise and fall of the amplitude, and phase, around Exceptional Points: a Scattering matrix approach

We analyze the behavior of a non-Hermitian opened one-dimensional quantum system with $\mathcal{PT}$ symmetry. This system is built by a dimer, with balanced gains and losses described by a parameter $γ$. By varying $γ$ the system resonances, which are naturally separated, coalesce at the exceptional point (EP). The transmission spectrum is obtained by means of the scattering matrix ($S$ matrix) formalism and we examine the wave functions corresponding to the resonances as a function of $γ$. Specifically, we look for the behavior and distribution of the phases of the $S$ matrix before, at and after the EP.

quant-ph↗

arXiv2021

Molecular orbitals of an elastic artificial benzene

Benzene, a hexagonal molecule with formula C$_6$H$_6$, is one of the most important aromatic hydrocarbons. Its structure arises from the $sp^{2}$ hybridization from which three in-plane $σ$-bonds are formed. A fourth $π$-orbital perpendicular to the molecular plane combines with those arising from other carbon atoms to form $π$-bonds, very important to describe the electronic properties of benzene. Here this $π$-system is emulated with elastic waves. The design and characterization of an artificial mechanical benzene molecule, composed of six resonators connected through finite phononic crystals, is reported. The latter structures trap the vibrations in the resonators and couple them through evanescent waves to neighboring resonators establishing a tight-binding regime for elastic waves. Our results show the appearance of a spectrum and wave amplitudes reminiscent of that of benzene. Finite element simulations and experimental data show excellent agreement with the Hückel model for benzene.

physics.atom-ph↗

arXiv2021

Deviations from Poisson statistics in the spectra of free rectangular thin plates

The counterintuitive fact that wave chaos appears in the bending spectrum of free rectangular thin plates is presented. After extensive numerical simulations, varying the ratio between the length of its sides, it is shown that (i) frequency levels belonging to different symmetry classes cross each other and (ii) for levels within the same symmetry sector, only avoided crossings appear. The consequence of anticrossings is studied by calculating the distributions of the ratio of consecutive level spacings for each symmetry class. The resulting ratio distribution disagrees with the expected Poissonian result. They are then compared with some well-known transition distributions between Poisson and the Gaussian orthogonal random matrix ensemble. It is found that the distribution of the ratio of consecutive level spacings agrees with the prediction of the Rosenzweig-Porter model. Also, the normal-mode vibration amplitudes are found experimentally on aluminum plates, before and after an avoided crossing for symmetrical-symmetrical, symmetrical-antisymmetrical, and antisymmetrical-symmetrical classes. The measured modes show an excellent agreement with our numerical predictions. The expected Poissonian distribution is recovered for the simply supported rectangular plate.

physics.class-ph↗

arXiv2019

Emulating tightly bound electrons in crystalline solids using mechanical waves

Solid state physics deals with systems composed of atoms with strongly bound electrons. The tunneling probability of each electron is determined by interactions that typically extend to neighboring sites, as their corresponding wave amplitudes decay rapidly away from an isolated atomic core. This kind of description is essential to material science, and it rules the electronic transport properties of metals, insulators and other condensed matter systems. The corresponding phenomenology is well captured by tight-binding models, where the electronic band structure emerges from atomic orbitals of isolated atoms plus their coupling to neighboring sites in a cristal. In this work, a mechanical system that emulates dynamically a tightly bound electron is built. This is done by connecting mechanical resonators via locally periodic aluminum bars acting as couplers. When the frequency of a particular resonator lies within the frequency gap of a coupler, the vibrational wave amplitude imitates a bound electron orbital. The localization of the wave at the resonator site and its exponential decay along the coupler are experimentally verified. The quantum dynamical tight-binding model and frequency measurements in mechanical structures show an excellent agreement.

cond-mat.mtrl-sci↗

arXiv2017

Mechanical Rainbow Trapping and Bloch Oscillations in Structured Elastic Beams

We demonstrate, both experimentally and numerically, the mechanical rainbow trapping effect and the mechanical Bloch oscillations for torsional waves propagating in chirped mechanical beams. After extensive simulations, three quasi-one-dimensional chirped structures were designed, constructed and experimentally characterized by Doppler spectroscopy. When the chirp intensity vanishes a perfect periodic system, with bands and gaps, is obtained. The mechanical rainbow trapping effect occurs for small values of the chirp intensity. The wave packet traveling along the beam is progressively slowing down and is reflected back at a certain depth, which depends on its central frequency. In this case a new kind of oscillation, here named "{\em rectified rainbow-Bloch oscillation}", appears since the wave packet is reflected at one side by the interface between the structure and the uniform rod and by the minigap at the opposite side. For larger values of the chirp parameter the rainbow trapping yields the penetration length where the mechanical Bloch oscillations emerge. Numerical simulations based on the transfer matrix method are in agreement with experimental data.

physics.app-ph↗

arXiv2016

In-plane vibrations of a rectangular plate: plane wave expansion modelling and experiment

Theoretical and experimental results for in-plane vibrations of a uniform rectangular plate with free boundary conditions are obtained. The experimental setup uses electromagnetic-acoustic transducers and a vector network analyzer. The theoretical calculations were obtained using the plane wave expansion method applied to the in-plane thin plate vibration theory. The agreement between theory and experiment is excellent for the lower 95 modes covering a very wide frequency range from DC to 20 kHz. Some measured normal-mode wave amplitudes were compared with the theoretical predictions; very good agreement was observed. The excellent agreement of the classical theory of in-plane vibrations confirms its reliability up to very high frequencies.

cond-mat.other↗

arXiv2015

Testing quantum transport without decoherence

The coherent electronic transport phenomena through quantum devices is difficult to observe due to thermal smearing and dephasing, the latter induced by inelastic scattering by phonons or impurities. In other wave systems, the temperature and dephasing may not destroy the coherence and can then be used to observe the underlying wave behaviour of the coherent quantum phenomena. Here, we observe coherent transmission of mechanical waves through a two-dimensional elastic Sinai billiard with two waveguides. The flexural-wave transmission performed by non-contact means, shows the transmission quantization when a new mode becomes open. In contrast with the quantum counterpart, these measurements agree with the theoretical predictions of the simplest model at zero temperature highlighting the universal character of the transmission fluctuations.

cond-mat.mtrl-sci↗

arXiv2015

Electromagnetic prompt response in an elastic wave cavity

A rapid, or prompt response, of an electromagnetic nature, is found in an elastic wave scattering experiment. The experiment is performed with torsional elastic waves in a quasi-one-dimensional cavity with one port, formed by a notch grooved at a certain distance from the free end of a beam. The stationary patterns are diminished using a passive vibration isolation system at the other end of the beam. The measurement of the resonances is performed with non-contact electromagnetic-acoustic transducers outside the cavity. In the Argand plane, each resonance describes a circle over a base impedance curve which comes from the electromagnetic components of the equipment. A model, based on a variation of Poisson's kernel is developed. Excellent agreement between theory and experiment is obtained.

nlin.CD↗

arXiv2013

Acoustic resonance spectroscopy for the advanced undergraduate laboratory

We present a simple experiment that allows advanced undergraduates to learn the principles and applications of spectroscopy. The technique, known as acoustic resonance spectroscopy, is applied to study a vibrating rod. The setup includes electromagnetic-acoustic transducers, an audio amplifier and a vector network analyzer. Typical results of compressional, torsional and bending waves are analyzed and compared with analytical results.

physics.ed-ph↗

arXiv2013

Scattering of Elastic Waves in a Quasi-one-dimensional Cavity: Theory and Experiment

We study the scattering of torsional waves through a quasi-one-dimensional cavity both, from the experimental and theoretical points of view. The experiment consists of an elastic rod with square cross section. In order to form a cavity, a notch at a certain distance of one end of the rod was grooved. To absorb the waves, at the other side of the rod, a wedge, covered by an absorbing foam, was machined. In the theoretical description, the scattering matrix S of the torsional waves was obtained. The distribution of S is given by Poisson's kernel. The theoretical predictions show an excellent agreement with the experimental results. This experiment corresponds, in quantum mechanics, to the scattering by a delta potential, in one dimension, located at a certain distance from an impenetrable wall.

cond-mat.mes-hall↗

arXiv2012

On the reliability of voting processes: the Mexican case

Analysis of vote distributions using current tools from statistical physics is of increasing interest. While data considered for physics studies are subject to a careful understanding of error sources, such analysis are almost absent in studies of voting process. As a way to test reliability in electoral processes we choose to investigate the July 2006 presidential election in Mexico. We use records which appeared in the Programa de Resultados Preliminares, PREP, the program which offers electoral results as soon as they are captured. In order to contrast the results we used the congressional election data-set and the July 2000 presidential record. We demonstrate the existence of correlations in the percentage of votes and, we offer evidence of the strong influence of the PRI in the curious results in the presidential case. Distributions of errors in the data-sets are analyzed for all the elections and no large deviations were found. That is, even when the sum of errors is around 45% in all cases, their global behavior is similar. This result gives support to the thesis of no large fraud for the July 2006 presidential election. Distribution of votes in all cases is obtained for all the parties. Parties and candidates with few votes, annulled votes and non-registered candidates follow a power law distribution, and the corporate party follows a daisy model distribution. Parties and candidates with many votes show a mixed behavior.

physics.soc-ph↗

arXiv2011

Absorption and Direct Processes in Chaotic Wave Scattering

Recent results on the scattering of waves by chaotic systems with losses and direct processes are discussed. We start by showing the results without direct processes nor absorption. We then discuss systems with direct processes and lossy systems separately. Finally the discussion of systems with both direct processes and loses is given. We will see how the regimes of strong and weak absorption are modified by the presence of the direct processes.

cond-mat.mes-hall↗