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R. A. Méndez-Sánchez

Publications and source records attributed to R. A. Méndez-Sánchez.

At least 19 recordsLinked to original sources
arXiv2025

Band Structure Engineering of Coupled-Resonator Phononic Polyacetylene and Polyaminoborane

A methodology for constructing a quasi-one-dimensional coupled-resonator phononic metamaterial is presented. This is achieved through the design of artificial phononic analogs of two molecular structures: trans-polyacetylene and trans-polyaminoborane. The band structure of trans-polyacetylene is analyzed in relation to the Su-Schrieffer-Heeger (SSH) model, while that of trans-polyaminoborane is examined using the $κ$-deformed Dirac equation, both within a tight-binding framework. Additionally, the obtained finite realization of the artificial trans-polyacetylene exhibits topologically protected states.

cond-mat.mtrl-sci↗
arXiv2024

Thermal transport of flexural phonons in a rectangular wire

We study the quantum thermal transport of elastic excitations through a two-dimensional elastic waveguide between two thermal reservoirs. We solve the classical Kirchhoff-Love equation for rectangular wires and explore the dispersion relation for both the symmetric and antisymmetric solutions. Then, we study the phonon transport of these modes within the second quantization framework by analyzing the mean quadratic displacement, from which the energy density current, the temperature field, and conductance are determined. We identify the relevant modes contributing to thermal transport and explore the average temperature difference to reach the high-temperature limit. We expect our results to pave the way for understanding phonon-mediated thermal transport in two-dimensional mesoscopic quantum devices.

cond-mat.mes-hall↗
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↗
arXiv2020

Sound field radiated by a rod

We study the acoustical intensity field radiated by a thin cylindrical rod vibrating in its lowest compressional mode. Due to the cylindrical symmetry, the emitted field is measured in a radial plane of the rod which is sufficient to reconstruct the full three-dimensional field. Starting from the one-dimensional approximation of the excited compressional mode, we develop a simplified theoretical wave equation which allows for a semi-analytical solution for the emitted wave field. The agreement between the experimental results and the semi-analytical solution is eloquent.

physics.app-ph↗
arXiv2019

On the electronic structure of benzene and borazine: An algebraic description

The spectrum of a hexagonal ring is analysed using concepts of group theory and a tight-binding model with first, second and third neighbours. The two doublets in the spectrum are explained with the $C_3$ symmetry group together with time-reversal symmetry. Degeneracy lifts are induced by means of various mechanisms. Conjugation symmetry breaking is introduced via magnetic fields, while $C_3$ breaking is studied with the introduction of defects, similar to the inclusion of fluorine atoms. Concrete applications to benzene and borazine are shown to illustrate the generality of our description. Wave functions are described in connection with partial or full aromaticity. Electronic density currents are found for all cases. A detailed study of a supersymmetry in a $6$-ring is presented and its consequences on electronic spectra are discussed.

physics.chem-ph↗
arXiv2019

Experimental validation of the theoretical prediction for the optical $S$ matrix

Scattering of waves is omnipresent in nature in systems with sizes varying from $10^{-15}$ to $10^{25}$ m. Within this 40 orders of magnitude, in a great number of systems, the scattering can be separated in an averaged response that crosses rapidly the scattering region and a fluctuating delayed response. This fact is the basis of the optical model; the averaged response, represented by the optical matrix $\langle S\rangle$, is composed with the fluctuating part that can be taken as a random matrix. Although the optical model was developed more than 60 years ago, a theoretical prediction for the optical matrix was obtained until very recently. The validity of such prediction is experimentally demonstrated here. This is done studying the scattering of torsional waves in a quasi-1D elastic system in which a locally periodic system is built; the distribution of the scattering matrix is calculated completely free of parameters. In contradistinction to all previous works, in microwaves and in elasticity, in which the value of $\langle S\rangle$ is obtained from the experiment, here the theoretical prediction is used to compare with the experiment. Numerical simulations show that the theoretical value is still valid when strong disorder is present. Several applications of the theoretical expression for the optical matrix in other areas of physics are proposed. Possible extensions of this work are also discussed.

cond-mat.dis-nn↗
arXiv2017

Analytical prediction for the optical matrix

Contrary to praxis, we provide an analytical expression, for a physical locally periodic structure, of the average $\langle S\rangle$ of the scattering matrix, called optical $S$ matrix in the nuclear physics jargon, and fundamentally present in all scattering processes. This is done with the help of a strictly analogous nonlinear dynamical mapping where iteration time is the number $N$ of scatterers. The ergodic property of chaotic attractors implies the existence and analyticity of $\langle S\rangle$. We find that the optical $S$ matrix depends only on the transport properties of a single cell, and that the Poisson kernel is the distribution of the scattering matrix $S_N$ in the large size limit $N\rightarrow \infty$. The theoretical distribution shows perfect agreement with numerical results for a chain of delta potentials. A consequence of our findings is the a priori knowledge of $\langle S\rangle$ without resort to experimental data.

cond-mat.stat-mech↗
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

Wave systems with direct processes and localized losses or gains: the non-unitary Poisson kernel

We study the scattering of waves in systems with losses or gains simulated by imaginary potentials. This is done for a complex delta potential that corresponds to a spatially localized absorption or amplification. In the Argand plane the scattering matrix moves on a circle $C$ centered on the real axis, but not at the origin, that is tangent to the unit circle. From the numerical simulations it is concluded that the distribution of the scattering matrix, when measured from the center of the circle $C$, agrees with the non-unitary Poisson kernel. This result is also obtained analytically by extending the analyticity condition, of unitary scattering matrices, to the non-unitary ones. We use this non-unitary Poisson kernel to obtain the distribution of non-unitary scattering matrices when measured from the origin of the Argand plane. The obtained marginal distributions have an excellent agreement with the numerical results.

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↗
arXiv2012

Anderson Localization in Disordered Vibrating Rods

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are exponentially localized as occurs in disordered solids. The localization length is measured using these wave amplitudes and it is shown to decrease as a function of frequency. The normal-mode spectrum is also measured as well as computed, so its level statistics can be analyzed. Fitting the nearest-neighbor spacing distribution a level repulsion parameter is defined that also varies with frequency. The localization length can then be expressed as a function of the repulsion parameter. There exists a range in which the localization length is a linear function of the repulsion parameter, which is consistent with Random Matrix Theory. However, at low values of the repulsion parameter the linear dependence does not hold.

nlin.CD↗