arXiv subjects

J. A. Méndez-Bermúdez

Publications and source records attributed to J. A. Méndez-Bermúdez.

At least 37 records · Page 2Linked to original sources

arXiv2019

Geometrical and spectral study of $β$-skeleton graphs

We perform an extensive numerical analysis of $β$-skeleton graphs, a particular type of proximity graphs. In a $β$-skeleton graph (BSG) two vertices are connected if a proximity rule, that depends of the parameter $β\in(0,\infty)$, is satisfied. Moreover, for $β>1$ there exist two different proximity rules, leading to lune-based and circle-based BSGs. First, by computing the average degree of large ensembles of BSGs we detect differences, which increase with the increase of $β$, between lune-based and circle-based BSGs. Then, within a random matrix theory (RMT) approach, we explore spectral and eigenvector properties of randomly weighted BSGs by the use of the nearest-neighbor energy-level spacing distribution and the entropic eigenvector localization length, respectively. The RMT analysis allows us to conclude that a localization transition occurs at $β=1$.

physics.soc-ph↗

arXiv2019

Multifractality in random networks with power-law decaying bond strengths

In this paper we demonstrate numerically that random networks whose adjacency matrices ${\bf A}$ are represented by a diluted version of the Power--Law Banded Random Matrix (PBRM) model have multifractal eigenfunctions. The PBRM model describes one--dimensional samples with random long--range bonds. The bond strengths of the model, which decay as a power--law, are tuned by the parameter $μ$ as $A_{mn}\propto |m-n|^{-μ}$; while the sparsity is driven by the average network connectivity $α$: for $α=0$ the vertices in the network are isolated and for $α=1$ the network is fully connected and the PBRM model is recovered. Though it is known that the PBRM model has multifractal eigenfunctions at the critical value $μ=μ_c=1$, we clearly show [from the scaling of the relative fluctuation of the participation number $I_2$ as well as the scaling of the probability distribution functions $P(\ln I_2)$] the existence of the critical value $μ_c\equiv μ_c(α)$ for $α<1$. Moreover, we characterise the multifractality of the eigenfunctions of our random network model by the use of the corresponding multifractal dimensions $D_q$, that we compute from the finite network-size scaling of the typical eigenfunction participation numbers $\exp\left\langle\ln I_q \right\rangle$.

physics.soc-ph↗

arXiv2018

Phenomenological approach to transport through three-terminal disordered wires

We study the voltage drop along three-terminal disordered wires in all transport regimes, from the ballistic to the localized regime. This is performed by measuring the voltage drop on one side of a one-dimensional disordered wire in a three-terminal set-up as a function of disorder. Two models of disorder in the wire are considered: (i) the one-dimensional Anderson model with diagonal disorder and (ii) finite-width bulk-disordered waveguides. Based on the known $β$-dependence of the voltage drop distribution of the three-terminal chaotic case, being $β$ the Dyson symmetry index ($β=1$, 2, and 4 for orthogonal, unitary, and symplectic symmetries, respectively), the analysis is extended to a continuous parameter $β>0$ and use the corresponding expression as a phenomenological one to reach the disordered phase. We show that our proposal encompasses all the transport regimes with $β$ depending linearly on the disorder strength.

cond-mat.mes-hall↗

arXiv2018

Distribution of S-matrix poles for one-dimensional disordered wires

By the use of the effective non-Hermitian Hamiltonian approach to scattering we study the distribution of the scattering matrix (S-matrix) poles in one-dimensional (1D) models with various types of diagonal disorder. We consider the case of 1D tight-binding wires, with both on-site uncorrelated and correlated disorder, coupled to the continuum through leads attached to the wire edges. In particular, we focus on the location of the S-matrix poles in the complex plane as a function of the coupling strength and the disorder strength. Specific interest is paid to the super-radiance transition emerging at the perfect coupling between wire and leads. We also study the effects of correlations intentionally imposed to the wire disorder.

cond-mat.dis-nn↗

arXiv2018

Cross-over in non-standard random-matrix spectral fluctuations without unfolding

Recently, the singular value decomposition (SVD) was applied to standard Gaussian ensembles of Random Matrix Theory (RMT) to determine the scale invariance in the spectral fluctuations without performing any unfolding procedure. Here, SVD is applied directly to the $ν$-Hermite ensemble and to a sparse matrix ensemble, decomposing the corresponding spectra in trend and fluctuation modes. In correspondence with known results, we obtain that fluctuation modes exhibit a cross-over between soft and rigid behavior. By using the trend modes we performed a data-adaptive unfolding, and we calculate traditional spectral fluctuation measures. Additionally, ensemble-averaged and individual-spectrum averaged statistics are calculated consistently within the same basis of normal modes.

nlin.CD↗

arXiv2018

Transport studies in three-terminal microwave graphs with orthogonal, unitary, and symplectic symmetry

The Landauer-Büttiker formalism establishes an equivalence between the electrical conduction through a device, e.g., a quantum dot, and the transmission. Guided by this analogy we perform transmission measurements through three-port microwave graphs with orthogonal, unitary, and symplectic symmetry thus mimicking three-terminal voltage drop devices. One of the ports is placed as input and a second one as output, while a third port is used as a probe. Analytical predictions show good agreement with the measurements in the presence of orthogonal and unitary symmetries, provided that the absorption and the influence of the coupling port are taken into account. The symplectic symmetry is realized in specifically designed graphs mimicking spin 1/2 systems. Again a good agreement between experiment and theory is found. For the symplectic case the results are marginally sensitive to absorption and coupling strength of the port, in contrast to the orthogonal and unitary case.

cond-mat.mes-hall↗

arXiv2016

Scaling Properties of Multilayer Random Networks

Multilayer networks are widespread in natural and manmade systems. Key properties of these networks are their spectral and eigenfunction characteristics, as they determine the critical properties of many dynamics occurring on top of them. In this paper, we numerically demonstrate that the normalized localization length $β$ of the eigenfunctions of multilayer random networks follows a simple scaling law given by $β=x^*/(1+x^*)$, with $x^*=γ(b_{\text{eff}}^2/L)^δ$, $γ,δ\sim 1$ and $b_{\text{eff}}$ being the effective bandwidth of the adjacency matrix of the network, whose size is $L=M\times N$. The reported scaling law for $β$ might help to better understand criticality in multilayer networks as well as to predict the eigenfunction localization properties of them.

physics.soc-ph↗

arXiv2016

Cross section versus time delay and trapping probability

We study the behavior of the $s$-wave partial cross section $σ(k)$, the Wigner-Smith time delay $τ(k)$, and the trapping probability $P(k)$ as function of the wave number $k$. The $s$-wave central square well is used for concreteness, simplicity, and to elucidate the controversy whether it shows true resonances. It is shown that, except for very sharp structures, the resonance part of the cross section, the trapping probability, and the time delay, reach their local maxima at different values of $k$. We show numerically that $τ(k)>0$ at its local maxima, occuring just before the resonant part of the cross section reaches its local maxima. These results are discussed in the light of the standard definition of resonance.

quant-ph↗

arXiv2014

Beyond Anderson Localization in 1D: Anomalous Localization of Microwaves in Random Waveguides

Experimental evidence demonstrating that anomalous localization of waves can be induced in a controllable manner is reported. A microwave waveguide with dielectric slabs randomly placed is used to confirm the presence of anomalous localization. If the random spacing between slabs follows a distribution with a power-law tail (Lévy-type distribution), unconventional properties in the microwave-transmission fluctuations take place revealing the presence of anomalous localization. We study both theoretically and experimentally the complete distribution of the transmission through random waveguides characterized by $α=1/2$ ("Lévy waveguides") and $α=3/4$, $α$ being the exponent of the power-law tail of the Lévy-type distribution. As we show, the transmission distributions are determined by only two parameters, both of them experimentally accessible. Effects of anomalous localization on the transmission are compared with those from the standard Anderson localization.

cond-mat.dis-nn↗

arXiv2013

Reflection resonances in surface-disordered waveguides: strong higher-order effects of the disorder

We study coherent wave scattering through waveguides with a step-like surface disorder and find distinct enhancements in the reflection coefficients at well-defined resonance values. Based on detailed numerical and analytical calculations, we can unambiguously identify the origin of these reflection resonances to be higher-order correlations in the surface disorder profile which are typically neglected in similar studies of the same system. A remarkable feature of this new effect is that it relies on the longitudinal correlations in the step profile, although individual step heights are random and thus completely uncorrelated. The corresponding resonances are very pronounced and robust with respect to ensemble averaging, and lead to an enhancement of wave reflection by more than one order of magnitude.

cond-mat.dis-nn↗

arXiv2003

From Chaos to Disorder in Quasi-1D Billiards with Corrugated Surfaces

We study chaotic properties of eigenstates depending on the degree of complexity in boundaries of a 2D periodic billiard. Main attention is paid to the situation when the motion of a classical particle is strongly chaotic. Our approach allows to explore the transition from deterministic to disordered chaos, and to link chaos to the degree of ergodicity in eigenstates of the billiard. We have found that bouncing balls strongly reduce chaotic properties of eigenstates, thus leading to a serious problem in statistical description for global properties of eigenstates. A quite unexpected effect of rough surfaces on the form of eigenstates has been discovered and explained by a strong localization of a subset of eigenstates in the energy representation.

cond-mat↗

arXiv2003

Amplitude and Gradient Scattering in Waveguides with Corrugated Surfaces

We study chaotic properties of eigenstates for periodic quasi-1D waveguides with "regular" and "random" surfaces. Main attention is paid to the role of the so-called "gradient scattering" which is due to large gradients in the scattering walls. We demonstrate numerically and explain theoretically that the gradient scattering can be quite strong even if the amplitude of scattering profiles is very small in comparison with the width of waveguides.

cond-mat.dis-nn↗

arXiv2003

Ballistic Localization in Quasi-1D Waveguides with Rough Surfaces

Structure of eigenstates in a periodic quasi-1D waveguide with a rough surface is studied both analytically and numerically. We have found a large number of "regular" eigenstates for any high energy. They result in a very slow convergence to the classical limit in which the eigenstates are expected to be completely ergodic. As a consequence, localization properties of eigenstates originated from unperturbed transverse channels with low indexes, are strongly localized (delocalized) in the momentum (coordinate) representation. These eigenstates were found to have a quite unexpeted form that manifests a kind of "repulsion" from the rough surface. Our results indicate that standard statistical approaches for ballistic localization in such waveguides seem to be unappropriate.

cond-mat.dis-nn↗

arXiv2003

Chaotic Waveguide-Based Resonators for Microlasers

We propose the construction of highly directional emission microlasers using two-dimensional high-index semiconductor waveguides as {\it open} resonators. The prototype waveguide is formed by two collinear leads connected to a cavity of certain shape. The proposed lasing mechanism requires that the shape of the cavity yield mixed chaotic ray dynamics so as to have the appropiate (phase space) resonance islands. These islands allow, via Heisenberg's uncertainty principle, the appearance of quasi bound states (QBS) which, in turn, propitiate the lasing mechanism. The energy values of the QBS are found through the solution of the Helmholtz equation. We use classical ray dynamics to predict the direction and intensity of the lasing produced by such open resonators for typical values of the index of refraction.

cond-mat.mes-hall↗

arXiv2002

Directional Emission from Microlasers with Open Chaotic Resonators

Using topological classical considerations (Poincarè Maps) the appearance of ``bow-tie''-shaped resonances is predicted for certain types of waveguides. The geometry of such waveguides is chosen to yield mixed chaotic dymnamics. Then, based on resonance effects, we propose the construction of directional emission microlasers using {\it open} chaotic semiconductor resonators of high refractive index.

cond-mat↗

arXiv2002

Some Thermal and Electrical Properties of Candelilla Wax

We report the values of some thermal and electrical properties of Candelilla Wax (euphorbia cerifera). The open-cell photoacoustic technique and another photothermic technique - based on the measure of the temperature decay of a heated sample - were employed to obtain the thermal diffusivity ($α_{s} = 0.026 \pm 0.00095 {cm}^{2}{/sec}$) as well as the thermal conductivity ($k=2.132 \pm 0.16 {W/mK}$) of this wax. The Kelvin null method was used to measure the dark decay of the surface potential of the sample after a Corona Discharge, obtaining a resistivity of $ρ_e=5.98 \pm 0.19 \times 10^{17} {ohm-cm}$.

cond-mat.mtrl-sci↗

arXiv2002

Understanding quantum scattering properties in terms of purely classical dynamics. 2D open chaotic billiards

We study classical and quantum scattering properties in the ballistic regime of particles in two-dimensional chaotic billiards that are models of electron- or micro- waveguides. To this end we construct the purely classical counterparts of the Scattering Probability (SP) matrix $\mid S_{n,m}\mid^2$ and Husimi distributions and specialize to the case of mixed chaotic motion. Comparison between classical and quantum quantities allows us to discover the purely classical dynamical origin of certain general, as well as particular features that appear in the quantum description of the system. On the other hand, at certain values of energy the tunneling of the wavefunction into classically forbidden regions produces striking differences between the classical and quantum quantities. We also see the manifestation of Whispering Gallery Orbits as a self-similar structure in the transmission part of the classical SP matrix. A potential application of this phenomenom in the field of microlasers is discussed briefly.

cond-mat.dis-nn↗

arXiv2001

Chaotic Electron Motion in Superlattices. Quantum-Classical Correspondence of the Structure of Eigenstates and LDOS

We investigate the classical-quantum correspondence for particle motion in a superlattice in the form of a 2D channel with periodic modulated boundaries. Its classical dynamics undergoes the generic transition to chaos of Hamiltonian systems as the amplitude of the modulation is increased. We show that for strong chaotic motion, the classical counterpart of the structure of eigenstates (SES) in energy space reveals an excellent agreement with the quantum one. This correspondence allows us to understand important features of the SES in terms of classical trajectories. We also show that for typical 2D modulated waveguides there exist, at any energy range, extremely localized eigenstates (in energy) which are practically unperturbed by the modulation. These states contribute to the strong fluctuations around the classical SES. The approach to the classical limit is discussed.

cond-mat.dis-nn↗