arXiv subjects

Sandra D. Prado

Publications and source records attributed to Sandra D. Prado.

15 recordsLinked to original sources

arXiv2026

Phase Transitions and Order Parameters in Correlation Matrices: A Wishart-Ensemble Perspective on the Largest Eigenvalue

We investigate the properties of the largest eigenvalue of correlation matrices within the framework of Wishart ensembles. In this work, we propose the largest eigenvalue as an effective empirical order parameter for detecting phase transitions in chaotic and spin systems, drawing an analogy between its derivatives and thermodynamic response functions derived from the free energy, however not necessarily linked to a critical divergence originally observed in the context of phase transitions theory.

cond-mat.stat-mech↗

arXiv2026

Universal spectral correlations in open Floquet systems with localized leaks

We show that introducing a localized leak in Floquet systems with time-reversal symmetry leads to universal spectral correlations governed by the non-Hermitian symmetry class $\mathrm{AI}^{\dagger}$, associated with complex-symmetric Ginibre random matrices, rather than by the unconstrained Ginibre ensemble. As a concrete example, we analyze the leaky quantum standard map (L-QSM) of the kicked rotor. Since the closed map exhibits circular orthogonal ensemble (COE) statistics, the open system is naturally compared with the truncated circular orthogonal ensemble (TCOE), which models localized leakage by removing columns from a COE matrix. We find excellent agreement between the bulk spectral properties of the L-QSM and the TCOE, and demonstrate that their short-range spectral correlations follow the universal statistics of the non-Hermitian symmetry class $\mathrm{AI}^{\dagger}$. This agreement holds for smaller leak sizes as the matrices increase, while the COE limit is recovered only when the truncation is smaller than one full column. In contrast to local properties, the global density of states of the L-QSM and the TCOE approaches the Ginibre circular law only when the leakage becomes sufficiently strong.

cond-mat.stat-mech↗

arXiv2024

Identifying Patterns Using Cross-Correlation Random Matrices Derived from Deterministic and Stochastic Differential Equations

Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C, 2350061 (2023)], which is directly reflected in the eigenvalues of these matrices. When these evolutions are analyzed in the mean-field regime, an important question arises: Can the Langevin equation, when translated into maps, perform the same function? Some studies suggest that this method may also capture the chaotic behavior of certain systems. In this work, we propose that the spectral properties of random matrices constructed from maps derived from deterministic or stochastic differential equations can indicate the critical or chaotic behavior of such systems. For chaotic systems, we need only the evolution of iterated Hamiltonian equations, and for spin systems, the Langevin maps obtained from mean-field equations suffice, thus avoiding the need for Monte Carlo (MC) simulations or other techniques.

cond-mat.stat-mech↗

arXiv2024

Effects of stickiness on the quantum states of strongly chaotic open systems

We investigate the effects of classical stickiness (orbits temporarily confined to a region of the chaotic phase space) to the structures of the quantum states of an open system. We consider the standard map of the kicked rotor and verify that regions of stickiness survive in the strong chaotic regime of the closed classical map. By scanning the system's phase space with a leak, we analyze how stickiness affects the degree of localization of the states of the quantum system. We find an excellent correspondence between the classical dwell time and finite-time Lyapunov exponents with the quantum dwell time and Wehrl entropy of the quantum states. Our approach suggests that knowledge of the structure of the classically chaotic trajectories can be used to determine where to place the leak to enhance or decrease the degree of delocalization of the quantum states.

quant-ph↗

arXiv2024

Efficient Computational method using random matrices describing critical thermodynamics

Our research highlights the effectiveness of utilizing matrices akin to Wishart matrices, derived from magnetization time series data under specific dynamics, to elucidate phase transitions and critical phenomena in the Q-state Potts model. By employing appropriate statistical methods, we not only discern second-order transitions but also differentiate weaker first-order transitions through careful analysis of the density of eigenvalues and their fluctuations. Furthermore, we investigate the method's sensitivity to stronger first-order transition points. Importantly, we establish a robust correlation between the system's actual thermodynamics and the spectral thermodynamics encapsulated within the eigenvalues. Our findings are further substantiated by correlation histograms of the time series data, revealing insightful patterns. Expanding upon our core findings, we present a didactic analysis that draws parallels between the spectral properties of criticality in a spin system and matrices intentionally imbued with correlations (a toy model). Within this framework, we observe a universal behavior characterized by the distribution of eigenvalues into two distinct groups, separated by a gap dependent on the level of correlation, influenced by temperature-induced changes in the spin system.

cond-mat.stat-mech↗

arXiv2024

A QAOA approach with fake devices: A case study for the maximum cut in ring graphs

The quantum approximate optimization algorithm (QAOA) can require considerable processing time for developers to test and debug their codes on expensive quantum devices. One avenue to circumvent this difficulty is to use the error maps of quantum devices, where a local simulator can be automatically configured to mimic an actual device backend. In our work, we evaluated some error maps of quantum devices, known as fake devices, that are freely available in the cloud. The QAOA and the problem of maximum cut in 2-regular connected graphs, known as ring of disagrees, were used as tools for the noise analysis. The approximation ratio, the expectation energy and the probability of success for this problem have been evaluated in two scenarios. First, the quantities were studied through noisy simulations using fake devices. Second, error mitigation methods such as optimization levels and translation (connectivity mapping) of the original problem were applied. These results were then compared with the analytical solution of the ring graph. The study shows that error mitigation methods were crucial in obtaining better results for the expectation value of the energy, the approximation ratio, and the probability of success for the ring graphs.

quant-ph↗

arXiv2024

Statistical properties of speckle patterns for a random number of scatterers and nonuniform phase distributions

The statistical properties of speckle patterns have important applications in optics, oceanography, and transport phenomena in disordered systems. Here we obtain closed-form analytic results for the amplitude distribution of speckle patterns formed by a random number of partial waves characterized by an arbitrary phase distribution, generalizing classical results of the random walk theory of speckle patterns. We show that the functional form of the amplitude distribution is solely determined by the distribution of the number of scatterers, while the phase distribution only influences the scale parameters. In the case of a non-random number of scatterers, we find an analytic expression for the amplitude distribution that extends the Rayleigh law to non-uniform random phases. For a negative binomial distribution of the number of scatterers, our results reveal that large fluctuations of the wave amplitudes become more pronounced in the case of biased random phases. We present numerical results that fully support our analytic findings.

physics.optics↗

arXiv2023

Exploring Transition from Stability to Chaos through Random Matrices

This study explores the application of random matrices to track chaotic dynamics within the Chirikov standard map. Our findings highlight the potential of matrices exhibiting Wishart-like characteristics, combined with statistical insights from their eigenvalue density, as a promising avenue for chaos monitoring. Inspired by a technique originally designed for detecting phase transitions in spin systems, we successfully adapt and apply it to identify analogous transformative patterns in the context of the Chirikov standard map. Leveraging the precision previously demonstrated in localizing critical points within magnetic systems in our prior research, our method accurately pinpoints the Chirikov resonance-overlap criterion for the chaos boundary at $K\approx 2.43$, reinforcing its effectiveness.

nlin.CD↗

arXiv2023

Mean-field criticality explained by random matrices theory

How a system initially at infinite temperature responds when suddenly placed at finite temperatures is a way to check the existence of phase transitions. It has been shown in [R. da Silva, IJMPC 2023] that phase transitions are imprinted in the spectra of matrices built from time evolutions of magnetization of spin models. In this paper, we show that this method works very accurately in determining the critical temperature in the mean-field Ising model. We show that for Glauber or Metropolis dynamics, the average eigenvalue has a minimum at the critical temperature, which is corroborated by an inflection at eigenvalue dispersion at this same point. Such transition is governed by a gap in the density of eigenvalues similar to short-range spin systems. We conclude that the thermodynamics of this mean-field system can be described by the fluctuations in the spectra of Wishart matrices which suggests a direct relationship between thermodynamic fluctuations and spectral fluctuations.

cond-mat.stat-mech↗

arXiv2019

Superextreme Waves Generation in the Linear Regime

Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been considered a necessary ingredient to generate superextreme waves, i.e., an enhanced wave amplification, where the wave amplitudes exceed by far those of standard rogue waves. Here we show, experimentally and theoretically, that superextreme optical waves emerge in the simple case of linear one-dimensional light diffraction. The underlying physics is a long-range correlation on the random initial phases of the light waves. When subgroups of random phases appear recurrently along the spatial phase distribution, a more ordered phase structure greatly increases the probability of constructive interference to generate superextreme events, i.e., non-Gaussian statistics with super-long tails. Our results consist of a significant advance in the understanding of extreme waves formation by linear superposition of random waves, with applications in a large variety of wave systems.

physics.optics↗

arXiv2019

A simple study of the correlation effects in the superposition of waves of electric fields: the emergence of extreme events

In this paper, we study the effects of correlated random phases in the intensity of a superposition of $N$ wave-fields. Our results suggest that regardless of whether the phase distribution is continuous or discrete if the phases are random correlated variables, we must observe a heavier tail distribution and the emergence of extreme events as the correlation between phases increases. We believe that such a simple method can be easily applied in other situations to show the existence of extreme statistical events in the context of nonlinear complex systems.

stat.AP↗

arXiv2017

A new look on the stabilization of inverted pendulum with parametric excitation and large random frequencies: analytical and numerical approaches

In this paper we explore the stability of an inverted pendulum with generalized parametric excitation described by a superposition of $N$ sines with different frequencies and phases. We show that when the amplitude is scaled with the frequency we obtain the stabilization of the real inverted pendulum, i.e., with values of $g$ according to planet Earth ($g\approx 9.8$m/s$^{2}$) for high frequencies. By randomly sorting the frequencies, we obtain a critical amplitude in light of perturbative theory in classical mechanics which is numerically tested by exploring its validity regime in many alternatives. We also analyse the effects when different values of $N$ as well as the pendulum size $l$ are taken into account.

physics.class-ph↗

arXiv2016

Deterministic and stochastic aspects of the stability in an inverted pendulum under a generalized parametric excitation

In this paper, we explore the stability of an inverted pendulum under a generalized parametric excitation described by a superposition of $N$ cosines with different amplitudes and frequencies, based on a simple stability condition that does not require any use of Lyapunov exponent, for example. Our analysis is separated in 3 different cases: $N=1$, $N=2$, and $N$ very large. Our results were obtained via numerical simulations by fourth-order Runge Kutta integration of the non-linear equations. We also calculate the effective potential also for $N>2$. We show then that numerical integrations recover a wider region of stability that are not captured by the (approximated) analytical method. We also analyze stochastic stabilization here: firstly, we look the effects of external noise in the stability diagram by enlarging the variance, and secondly, when $N$ is large, we rescale the amplitude by showing that the diagrams for time survival of the inverted pendulum resembles the exact case for $N=1$. Finally, we find numerically the optimal number of cosines corresponding to the maximal survival probability of the pendulum.

physics.class-ph↗

arXiv2016

Temporal Network Analysis of Literary Texts

We study temporal networks of characters in literature focusing on "Alice's Adventures in Wonderland" (1865) by Lewis Carroll and the anonymous "La Chanson de Roland" (around 1100). The former, one of the most influential pieces of nonsense literature ever written, describes the adventures of Alice in a fantasy world with logic plays interspersed along the narrative. The latter, a song of heroic deeds, depicts the Battle of Roncevaux in 778 A.D. during Charlemagne's campaign on the Iberian Peninsula. We apply methods recently developed by Taylor and coworkers \cite{Taylor+2015} to find time-averaged eigenvector centralities, Freeman indices and vitalities of characters. We show that temporal networks are more appropriate than static ones for studying stories, as they capture features that the time-independent approaches fail to yield.

physics.soc-ph↗

arXiv2015

Light with tunable non-Markovian phase imprint

We introduce a simple and flexible method to generate spatially non-Markovian light with tunable coherence properties in one and two dimensions. The unusual behavior of this light is demonstrated experimentally by probing the far field and recording its diffraction pattern after a double slit: In both cases we observe instead of a central intensity maximum a line or cross shaped dark region, whose width and profile depend on the non-Markovian coherence properties. Since these properties can be controlled and easily reproduced in experiment, the presented approach lends itself to serve as a testbed to gain a deeper understanding of non-Markovian processes.

physics.optics↗