arXiv subjects

J. A. Méndez-Bermúdez

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

At least 19 recordsLinked to original sources

arXiv2026

Stochastic Web Map: Survival probability and escape frequency

We study transport and escape in the Stochastic Web Map (SWM), an area-preserving system with phase-space structure controlled by a symmetry parameter $q$ and nonlinearity $K$. By analyzing the survival probability $P_{\text{S}}(n)$ and escape frequency $P_{\text{E}}(\ln n)$, we show that in the chaotic regime escape dynamics is governed by a single time scale $n_{\text{typ}}\propto K^{-2}h^{2}$; here $h$ is the size of the escape horizon. Deviations at large $K$ and small $h$ indicate a breakdown of the quasilinear approximation. Then, upon rescaling the time by $n_{\text{typ}}$, escape statistics becomes universal, independent of $q$. These results demonstrate that escape is controlled by global transport rather than symmetry.

nlin.CD↗

arXiv2026

Survival probability of random networks

In this work we study in detail all phases of the time evolution of a delta-like excitation in Erdös-Renyi (ER) random networks by means of the survival probability (SP): The initial decay of the SP (both, the fast decay followed by the power-law decay), the correlation hole regime (the regime between the minimum value of the SP and its saturation value), and the saturation of the SP. Specifically, we found that (i) the power-law decay of the SP and the time-averaged SP are proportional to $t^{-D_{2}}$ and $t^{-\widetilde{D}_{2}}$, respectively (where $D_2$ and $\widetilde{D}_2$ are the correlation dimension of the eigenstates of the randomly weighted adjacency matrices of the ER random networks and the correlation dimension associated with the initial state, respectively) and (ii) the relative depth of the correlation hole of the SP scales with the average degree $\langle k\rangle\approx np$ (here, $n$ and $p$ are the size and the connection probability of the ER random networks). In addition, we show that the eigenstates of the randomly weighted adjacency matrices of ER networks display clear multifractal properties.

cond-mat.stat-mech↗

arXiv2025

On the distribution of topological and spectral indices on random graphs

We perform a detailed statistical study of the distribution of topological and spectral indices on random graphs $G=(V,E)$ in a wide range of connectivity regimes. First, we consider degree-based topological indices (TIs), and focus on two classes of them: $X_Σ(G) = \sum_{uv \in E} f(d_u,d_v)$ and $X_Π(G) = \prod_{uv \in E} g(d_u,d_v)$, where $uv$ denotes the edge of $G$ connecting the vertices $u$ and $v$, $d_u$ is the degree of the vertex $u$, and $f(x,y)$ and $g(x,y)$ are functions of the vertex degrees. Specifically, we apply $X_Σ(G)$ and $X_Π(G)$ on Erdös-Rényi graphs and random geometric graphs along the full transition from almost isolated vertices to mostly connected graphs. While we verify that $P(X_Σ(G))$ converges to a standard normal distribution, we show that $P( X_Π(G))$ converges to a log-normal distribution. In addition we also analyze Revan-degree-based indices and spectral indices (those defined from the eigenvalues and eigenvectors of the graph adjacency matrix). Indeed, for Revan-degree indices, we obtain results equivalent to those for standard degree-based TIs. Instead, for spectral indices, we report two distinct patterns: the distribution of indices defined only from eigenvalues approaches a normal distribution, while the distribution of those indices involving both eigenvalues and eigenvectors approaches a log-normal distribution.

math.CO↗

arXiv2025

Universal properties of Wigner delay times and resonance widths of tight-binding random graphs

The delay experienced by a probe due to interactions with a scattering media is highly related to the internal dynamics inside that media. This property is well captured by the Wigner delay time and the resonance widths. By the use of the equivalence between the adjacency matrix of a random graph and the tight-binding Hamiltonian of the corresponding electronic media, the scattering matrix approach to electronic transport is used to compute Wigner delay times and resonance widths of Erdös-Rényi graphs and random geometric graphs, including bipartite random geometric graphs. In particular, the situation when a single-channel lead attached to the graphs is considered. Our results show a smooth crossover towards universality as the graphs become complete. We also introduce a parameter $ξ$, depending on the graph average degree $\langle k \rangle$ and graph size $N$, that scales the distributions of both Wigner delay times and resonance widths; highlighting the universal character of both distributions. Specifically, $ξ= \langle k \rangle N^{-α}$ where $α$ is graph-model dependent.

cond-mat.dis-nn↗

arXiv2024

Multilayer directed random networks: Scaling of spectral properties

Motivated by the wide presence of multilayer networks in both natural and human-made systems, within a random matrix theory (RMT) approach, in this study we compute eigenfunction and spectral properties of multilayer directed random networks (MDRNs) in two setups composed by $M$ layers of size $N$: A line and a complete graph (node-aligned multiplex network). First, we numerically demonstrate that the normalized localization length $β$ of the eigenfunctions of MDRNs follows a simple scaling law given by $β=x^*/(1+x^*)$, with $x^*\propto (b_{\rm eff}^2/L)^δ$, $δ\sim 1$ and $b_{\rm eff}$ being the effective bandwidth of the adjacency matrix of the network of size $L=M\times N$. Here, $b_{\rm eff}$ incorporates both intra- and inter-layer edges. Then, we show that other eigenfunction and spectral RMT measures (the inverse participation ratio of eigenfunctions, the ratio between nearest- and next-to-nearest-neighbor eigenvalue distances, and the ratio between consecutive singular-value spacings) of MDRNs also scale with $x^*$.

cond-mat.dis-nn↗

arXiv2023

Topological and spectral properties of random digraphs

We investigate some topological and spectral properties of Erdős-Rényi (ER) random digraphs $D(n,p)$. In terms of topological properties, our primary focus lies in analyzing the number of non-isolated vertices $V_x(D)$ as well as two vertex-degree-based topological indices: the Randić index $R(D)$ and sum-connectivity index $χ(D)$. First, by performing a scaling analysis we show that the average degree $\langle k \rangle$ serves as scaling parameter for the average values of $V_x(D)$, $R(D)$ and $χ(D)$. Then, we also state expressions relating the number of arcs, spectral radius, and closed walks of length 2 to $(n,p)$, the parameters of ER random digraphs. Concerning spectral properties, we compute six different graph energies on $D(n,p)$. We start by validating $\langle k \rangle$ as the scaling parameter of the graph energies. Additionally, we reformulate a set of bounds previously reported in the literature for these energies as a function $(n,p)$. Finally, we phenomenologically state relations between energies that allow us to extend previously known bounds.

cond-mat.dis-nn↗

arXiv2023

Universal insulating-to-metallic crossover in tight-binding random geometric graphs

Within the scattering matrix approach to electronic transport, the scattering and transport properties of tight-binding random graphs are analyzed. In particular, we compute the scattering matrix elements, the transmission, the channel-to-channel transmission distributions (including the total transmission distribution), the shot noise power, and the elastic enhancement factor. Two graph models are considered: random geometric graphs and bipartite random geometric graphs. The results show an insulating to a metallic crossover in the scattering and transport properties by increasing the average degree of the graphs from small to large values. Also, the scattering and transport properties are shown to be invariant under a scaling parameter depending on the average degree and the graph size. Furthermore, for large connectivity and in the perfect coupling regime, the scattering and transport properties of both graph models are well described by the random matrix theory predictions of electronic transport, except for bipartite graphs in particular scattering setups.

cond-mat.dis-nn↗

arXiv2023

Scattering and transport properties of the three classical Wigner-Dyson ensembles at the Anderson transition

An extensive numerical analysis of the scattering and transport properties of the power-law banded random matrix model (PBRM) at criticality in the presence of orthogonal, unitary, and symplectic symmetries is presented. Our results show a good agreement with existing analytical expressions in the metallic regime and with heuristic relations widely used in studies of the PBRM model in the presence of orthogonal and unitary symmetries. Moreover, our results confirm that the multifractal behavior of disordered systems at criticality can be probed by measuring scattering and transport properties, which is of paramount importance from the experimental point of view. Thus, a full picture of the scattering and transport properties of the PBRM model at criticality corresponding to the three classical Wigner-Dyson ensembles is provided.

cond-mat.dis-nn↗

arXiv2022

Time delay in 1D disordered media with high transmission

We study the time delay of reflected and transmitted waves in 1D disordered media with high transmission. Highly transparent and translucent random media are found in nature or can be synthetically produced. We perform numerical simulations of microwaves propagating in disordered waveguides to show that reflection amplitudes are described by complex Gaussian random variables with the remarkable consequence that the time-delay statistics in reflection of 1D disordered media are described as in random media in the diffusive regime. For transmitted waves, we show numerically that the time delay is an additive quantity and its fluctuations thus follow a Gaussian distribution. Ultimately, the distributions of the time delay in reflection and transmission are physical illustrations of the central limit theorem at work.

cond-mat.dis-nn↗

arXiv2021

Microwave graphs analogs for the voltage drop in three-terminal devices with orthogonal, unitary and symplectic symmetry

Transmission measurements through three-port microwave graphs are performed in a symmetric setting, in analogy to three-terminal voltage drop devices with orthogonal, unitary, and symplectic symmetry. The terminal used as a probe is symmetrically located between two chaotic graphs, each graph is connected to one port, the input and the output, respectively. The analysis of the experimental data exhibit the weak localization and antilocalization phenomena in a clear fashion. We find a good agreement with theoretical predictions, provided that the effect of dissipation and imperfect coupling to the ports are taken into account.

cond-mat.other↗

arXiv2021

Disorder-Enhanced and Disorder-Independent Transport with Long-Range Hopping: Application to Molecular Chains in Optical Cavities

Overcoming the detrimental effect of disorder at the nanoscale is very hard since disorder induces localization and an exponential suppression of transport efficiency. Here we unveil novel and robust quantum transport regimes achievable in nanosystems by exploiting long-range hopping. We demonstrate that in a 1D disordered nanostructure in the presence of long-range hopping, transport efficiency, after decreasing exponentially with disorder at first, is then enhanced by disorder [disorder-enhanced transport (DET) regime] until, counterintuitively, it reaches a disorder-independent transport (DIT) regime, persisting over several orders of disorder magnitude in realistic systems. To enlighten the relevance of our results, we demonstrate that an ensemble of emitters in a cavity can be described by an effective long-range Hamiltonian. The specific case of a disordered molecular wire placed in an optical cavity is discussed, showing that the DIT and DET regimes can be reached with state-of-the-art experimental setups.

quant-ph↗

arXiv2021

On the multifractal dimensions and statistical properties of critical ensembles characterized by the three classical Wigner-Dyson symmetry classes

We introduce a power-law banded random matrix model for the third of the three classical Wigner-Dyson ensembles, i.e., the symplectic ensemble. A detailed analysis of the statistical properties of its eigenvectors and eigenvalues, at criticality, is presented. This ensemble is relevant for time-reversal symmetric systems with strong spin-orbit interaction. For the sake of completeness, we also review the statistical properties of eigenvectors and eigenvalues of the power-law random banded matrix model for the corresponding systems in the presence and absence of time reversal invariance, previously considered in the literature. Our results show a good agreement with heuristic relations for the eigenstate and eigenenergy statistics at criticality, proposed in previous studies. With this, we provide a full picture of the power-law random banded matrix model corresponding to the three classical Wigner-Dyson ensembles.

cond-mat.dis-nn↗

arXiv2021

Statistical properties of mutualistic-competitive random networks

Mutualistic networks are used to study the structure and processes inherent to mutualistic relationships. In this paper, we introduce a random matrix ensemble (RME) representing the adjacency matrices of mutualistic networks composed by two vertex sets of sizes $n$ and $m-n$. Our RME depends on three parameters: the network size $n$, the size of the smaller set $m$, and the connectivity between the two sets $α$, where $α$ is the ratio of current adjacent pairs over the total number of possible adjacent pairs between the sets. We focus on the the spectral, eigenvector and topological properties of the RME by computing, respectively, the ratio of consecutive eigenvalue spacings $r$, the Shannon entropy of the eigenvectors $S$, and the Randić index $R$. First, within a random matrix theory approach (i.e., a statistical approach), we identify a parameter $ξ\equivξ(n,m,α)$ that scales the average normalized measures $\left< \overline{X} \right>$ (with $X$ representing $r$, $S$ and $R$). Specifically, we show that (i) $ξ\propto αn$ with a weak dependence on $m$, and (ii) for $ξ<1/10$ most vertices in the mutualistic network are isolated, while for $ξ>10$ the network acquires the properties of a complete network, i.e., the transition from isolated vertices to a complete-like behavior occurs in the interval $1/10<ξ<10$. Then, we demonstrate that our statistical approach predicts reasonably well the properties of real-world mutualistic networks; that is, the universal curves $\left< \overline{X} \right>$ vs. $ξ$ show good correspondence with the properties of real-world networks.

cond-mat.dis-nn↗

arXiv2020

Delay time of waves performing Lévy walks in 1D random media

The time that waves spend inside 1D random media with the possibility of performing Lévy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered systems via the delay time. We show that a wide class of disorder--Lévy disorder--leads to strong random fluctuations of the delay time; nevertheless, some statistical properties such as the tail of the distribution and the average of the delay time are insensitive to Lévy walks. Our results reveal a universal character of wave propagation that goes beyond standard Brownian wave-diffusion.

cond-mat.dis-nn↗

arXiv2020

Spacing ratio characterization of the spectra of directed random networks

Previous literature on random matrix and network science has traditionally employed measures derived from nearest-neighbor level spacing distributions to characterize the eigenvalue statistics of random matrices. This approach, however, depends crucially on eigenvalue unfolding procedures, which in many situations represent a major hindrance due to constraints in the calculation, specially in the case of complex spectra. Here we study the spectra of directed networks using the recently introduced ratios between nearest- and next-to-nearest eigenvalue spacing, thus circumventing the shortcomings imposed by spectral unfolding. Specifically, we characterize the eigenvalue statistics of directed Erdős-Rényi (ER) random networks by means of two adjacency matrix representations; namely (i) weighted non-Hermitian random matrices and (ii) a transformation on non-Hermitian adjacency matrices which produces weighted Hermitian matrices. For both representations, we find that the distribution of spacing ratios becomes universal for a fixed average degree, in accordance with undirected random networks. Furthermore, by calculating the average spacing ratio as a function of the average degree, we show that the spectral statistics of directed ER random networks undergoes a transition from Poisson to Ginibre statistics for model (i) and from Poisson to Gaussian Unitary Ensemble statistics for model (ii). Eigenvector delocalization effects of directed networks are also discussed.

cond-mat.dis-nn↗

arXiv2020

Universality of eigenvector delocalization and the nature of the SIS phase transition in multiplex networks

Universal spectral properties of multiplex networks allow us to assess the nature of the transition between disease-free and endemic phases in the SIS epidemic spreading model. In a multiplex network, depending on a coupling parameter, $p$, the inverse participation ratio ($IPR$) of the leading eigenvector of the adjacency matrix can be in two different structural regimes: (i) layer-localized and (ii) delocalized. Here we formalize the structural transition point, $p^*$, between these two regimes, showing that there are universal properties regarding both the layer size $n$ and the layer configurations. Namely, we show that $IPR \sim n^{-δ}$, with $δ\approx 1$, and revealed an approximately linear relationship between $p^*$ and the difference between the layers' average degrees. Furthermore, we showed that this multiplex structural transition is intrinsically connected with the nature of the SIS phase transition, allowing us to both understand and quantify the phenomenon. As these results are related to the universal properties of the leading eigenvector, we expect that our findings might be relevant to other dynamical processes in complex networks.

physics.soc-ph↗

arXiv2019

Normal mode analysis of spectra of random networks

Several spectral fluctuation measures of random matrix theory (RMT) have been applied in the study of spectral properties of networks. However, the calculation of those statistics requires performing an unfolding procedure, which may not be an easy task. In this work, network spectra are interpreted as time series, and we show how their short and long-range correlations can be characterized without implementing any previous unfolding. In particular, we consider three different representations of Erdös-Rényi (ER) random networks: standard ER networks, ER networks with random-weighted self-edges, and fully random-weighted ER networks. In each case, we apply singular value decomposition (SVD) such that the spectra are decomposed in trend and fluctuation normal modes. We obtain that the fluctuation modes exhibit a clear crossover between the Poisson and the Gaussian orthogonal ensemble statistics when increasing the average degree of ER networks. Moreover, by using the trend modes, we perform a data-adaptive unfolding to calculate, for comparison purposes, traditional fluctuation measures such as the nearest neighbor spacing distribution, number variance $Σ$2, as well as $Δ$3 and δn statistics. The thorough comparison of RMT short and long-range correlation measures make us identify the SVD method as a robust tool for characterizing random network spectra.

cond-mat.dis-nn↗

arXiv2019

Level Repulsion and Dynamics in the Finite One-Dimensional Anderson Model

This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest neighbor couplings. In the thermodynamic limit, all eigenstates of this model are exponentially localized in configuration space for any infinitesimal onsite disorder strength $W$. But this is not the case when the model is finite and the localization length is larger than the system size $L$, which is a picture that can be experimentally investigated. We analyze the degree of energy-level repulsion, the structure of the eigenstates, and the time evolution of the finite 1D Anderson model as a function of the parameter $ξ\propto (W^2 L)^{-1}$. As $ξ$ increases, all energy-level statistics typical of random matrix theory are observed. The statistics are reflected in the corresponding eigenstates and also in the dynamics. We show that the probability in time to find a particle initially placed on the first site of an open chain decays as fast as in full random matrices and much faster that when the particle is initially placed far from the edges. We also see that at long times, the presence of energy-level repulsion manifests in the form of the correlation hole. In addition, our results demonstrate that the hole is not exclusive to random matrix statistics, but emerges also for $W=0$, when it is in fact deeper.

cond-mat.dis-nn↗