Ernesto P. Raposo

Federal University of Pernambuco | UFPE

In this contribution, we investigate how to correctly describe sums of independent and identically distributed random velocities in the theory of special relativity. We derive a one-dimensional probability distribution of velocities stable under relativistic velocity addition. In a given system, this allows identifying distinct physical regimes in...

We apply the phenomenological renormalization group to resting-state fMRI time series of brain activity in a large population. By recursively coarse-graining the data, we compute scaling exponents for the series variance, log probability of silence, and largest covariance eigenvalue. The exponents clearly exhibit linear interdependencies, which we...

Spin glass theory, as a paradigm for describing disordered magnetic systems, constitutes a prominent subject of study within statistical physics. Replica symmetry breaking (RSB), as one of the pivotal concepts for the understanding of spin glass theory, means that under identical conditions, disordered systems can yield distinct states with nontriv...

Modulation of scattering in random lasers (RLs) by magnetic fields has attracted much attention due to its rich physical insights. We fabricate magnetic gain polymer optical fiber to generate RLs. From macroscopic experimental phenomena, with the increase of the magnetic field strength, the magnetic transverse photocurrent exists in disordered mult...

We report the first experimental demonstration of the replica symmetry breaking (RSB) phenomenon in a fiber laser system supporting standard mode-locking (SML) regime. Though theoretically predicted, this photonic glassy phase remained experimentally undisclosed so far. We employ an ytterbium-based mode-locked fiber laser with a very rich phase dia...

The numerical hailstone sequences, or orbits, generated by the Collatzmap have been disclosed to present relevant features commonly associated with complex systems. It is so despite the extreme simplicity of the arithmetic dynamical system iteration rule. Indeed, for a positive integer n, the Collatz map f reads f(n) = n/2 ( f(n) = 3n + 1) for n ev...

In this work, the RSB phase transition of Raman random fiber laser (RFL) is experimentally demonstrated, and the relationship between different modes of Raman RFL and RSB phase transition is explored for the first time.

We investigate the emergence of rogue quantum amplitudes in discrete-time quantum walks (DTQWs) influenced by phase disorder. Our study reveals the statistics of occupation probability amplitudes in space and time, uncovering optimal disorder regimes that favor rogue wave events. Through numerical simulations, we demonstrate that the probability of...

We investigate the evolution dynamics of inhomogeneous discrete-time one-dimensional quantum walks displaying long-range correlations in both space and time. The associated quantum coin operators of internal states are built to exhibit random inhomogeneity distribution of long-range correlations embedded in the time evolution protocol through a fra...

We investigate the replica symmetry breaking (RSB) phenomenon in random lasers (RLs) through Monte Carlo simulations employing photonic random walkers that diffuse and get randomly scattered in the active medium. The walkers interact not only with the population of excited atoms, but also among themselves, in a mean-field-type approach based on the...

Plasmodium sporozoites actively migrate in the dermis and enter blood vessels to infect the liver. Despite their importance for malaria infection, little is known about these cutaneous processes. We combine intravital imaging in a rodent malaria model and statistical methods to unveil the parasite strategy to reach the bloodstream. We determine tha...

We investigate the evolution dynamics of inhomogeneous discrete-time one-dimensional quantum walks displaying long-range correlations in both space and time. The associated quantum coin operators are built to exhibit a random inhomogeneity distribution of long-range correlations embedded in the time evolution protocol through a fractional Brownian...

We address the competing superconducting and magnetic phases on the honeycomb lattice, in a field-theoretic approach suitable to yield a low-energy perturbative theory for the strong-coupling limit of the Hubbard model, both at half filling and in the low and high hole-doped regimes. The effective low-lying Hamiltonian is presented in terms of char...

There is demand in diverse fields for a reliable method of estimating the entropy associated with correlations. The estimation of a unique entropy directly from the Pearson correlation matrix has remained an open problem for more than half a century. All existing approaches lack generality insofar as they require thresholding choices that arbitrari...

We apply a recently proposed modified Pearson correlation coefficient to investigate the statistical properties of intensity fluctuations in the second harmonic as well as fundamental mode of a multimode Q-switched Nd:yttrium aluminum garnet laser. Above threshold the system displays a photonic ferromagneticlike spontaneous mode-locking phase with...

Although heavy metal materials, due to their large spin-orbit interaction, would be expected to act as an efficient converter of spin current to charge current, Bismuth does not obey this rule. Heterostructures of yttrium iron garnet (YIG)/Bi are investigated by means of the spin pumping technique and the results show that Bi exhibits negligible sp...

The Lévy flight foraging hypothesis states that organisms must have evolved adaptations to exploit Lévy walk search strategies. Indeed, it is widely accepted that inverse square Lévy walks optimize the search efficiency in foraging with unrestricted revisits (also known as nondestructive foraging). However, a mathematically rigorous demonstration o...

An exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough, fomenting great prospects for further application, similarly to what happened when Lars Onsager solved the two...

We investigate the dependence on the search space dimension of statistical properties of random searches with Lévy α-stable and power-law distributions of step lengths. We find that the probabilities to return to the last target found (P0) and to encounter faraway targets (PL), as well as the associated Shannon entropy S, behave as a function of α...

We investigate the stochastic susceptible-infected-recovered (SIR) model of infectious disease dynamics in the Fock-space approach. In contrast to conventional SIR models based on ordinary differential equations for the subpopulation sizes of S, I, and R individuals, the stochastic SIR model is driven by a master equation governing the transition p...

Exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough, fomenting great prospects for further application, similarly to what happened when Lars Onsager solved the two di...

A photonic connection between turbulence and spin glasses has been recently established both theoretically and experimentally using a random fiber laser as a photonic platform. Besides unveiling this interplay, it links the works of two 2021 Nobel laureates in Physics.

We propose an approach based on random matrix theory to calculate the temporal second-order intensity correlation function g(2)(t ) of the radiation emitted by random lasers and random fiber lasers. The multimode character of these systems, with a relevant degree of disorder in the active medium, and a large number of random scattering centers subs...

We propose a new approach based on random matrix theory to calculate the temporal second-order intensity correlation function $g^{(2)}(t)$ of the radiation emitted by random lasers and random fiber lasers. The multimode character of these systems, with a relevant degree of disorder in the active medium, and large number of random scattering centers...

We study the pseudogap phase of cuprate superconducting systems in a Hartree–Fock approach to the Hubbard Hamiltonian with an extra competing next-nearest-neighbor hopping term of energy t2 along the nodal directions of the sublattice Brillouin zone. A maximum pseudogap energy of 101.08 meV is obtained at the nodal points of the Fermi surface in th...

Random lasers (RLs) are remarkable experimental platforms to advance the understanding of complex systems phenomena, such as the replica-symmetry-breaking (RSB) spin glass phase, dynamics modes correlations, and turbulence. Here we study these three phenomena jointly in a Nd:YAG based RL synthesized for the first time using a spray pyrolysis method...

The 2021 Physics Nobel Prize was awarded to Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi for their “groundbreaking contributions to our understanding of complex physical systems.” Here we review some of the ideas and results which served as the scientific basis to the award. We also comment on the works by our research group on the complex...

Random lasers are recognized as open cavity complex systems emitting coherent radiation with interesting properties. I shall describe its applications to studies of spin-glass, turbulence and its relation to the Nobel Prize in Physics 2021

Random lasers (RLs) are a special type of laser with a feedback mechanism arising from the random photon scattering in a disordered medium. Their emitted intensity is inherently stochastic. Here we compare results for the intensity distribution from two classes of models. The first concerns electromagnetic wave scattering in a random medium with fi...

The hybrid electronically addressable random (HEAR) laser is a novel type of random fiber laser that presents the remarkable property of selection of the fiber section with lasing emission. Here we present a joint analysis of the correlations between intensity fluctuations at distinct wavelengths and replica symmetry breaking (RSB) behavior of the...

We have extended the Fock space (FS) approach to address the relevant problem of evaluating the mean first passage time (MFPT) and absorption probabilities of a Lévy random particle in a discrete finite interval with absorbing boundaries. In this approach the master equation is cast in the form of a real-valued Schrödinger-like equation with a Hami...

Random Lasers (RLs) and Random Fiber Lasers (RFLs) have been the subject of intense research since their first experimental demonstration in 1994 and 2007, respectively. These low coherence light sources rely on multiple scattering of light to provide optical feedback in a medium combining a properly excited gain material and a scattering disordere...

We address the general problem of how to estimate an entropy given a Pearson correlation matrix. Most methods currently in use inject a degree of arbitrariness due to the thresholding of correlations. Here we propose an entirely objective method of entropy estimation that requires no thresholding. Let $\boldsymbol{R}$ be an $N\times N$ Pearson corr...

It is widely accepted that inverse square L\'evy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets when the search restarts in the vicinity of the previously visited target, which becomes revisitable again with high probability, i.e., non-destructive foraging [Natur...

Information on the relevant global scales of the search space, even if partial, should conceivably enhance the performance of random searches. Here we show numerically and analytically that the paradigmatic uninformed optimal Lévy searches can be outperformed by informed multiple-scale random searches in one (1D) and two (2D) dimensions, even when...

DOI:https://doi.org/10.1103/PhysRevLett.126.048901

The Collatz conjecture, perhaps the most elementary unsolved problem in mathematics, claims that for all positive integers n, the map n↦n/2 (n even) and n↦3n+1 (n odd) reaches 1 after a finite number of iterations. We examine the Collatz map's orbits, known as hailstone sequences, to determine whether or not they exhibit scale-invariant behavior, i...

High-order nonlinear optical effects have become an important feature of photonic systems, both ordered and disordered. In this work, a very large and robust set of experimental data obtained from the emission spectra of a trivalent neodymium ion-based random laser, whose action mechanism relies upon gain and disorder, was characterized in detail....

Amorphous FexZr100−x alloys display a complex magnetic phase diagram, particularly in the range 89% 􏰁 x 􏰁 93% in which the phase transition from the paramagnetic to a soft ferromagnetic (FM) state at a critical temperature Tc precedes a second transition at Txy < Tc to a transverse spin-glass (SG) phase, with frozen spin components transverse to th...

The statistical description of a one-dimensional superdiffusive Lévy flier restricted to a finite domain is well known to be technically involving. For example, in this type of process the probability distribution P(x, t) and survival probability S(t) cannot be obtained from the method of images. Other methods, such as the fractional derivative app...

Amorphous FexZr100−x alloys display a complex magnetic phase diagram, particularly in the range 89% x 93% in which the phase transition from the paramagnetic to a soft ferromagnetic (FM) state at a critical temperature Tc precedes a second transition at Txy < Tc to a transverse spin-glass (SG) phase, with frozen spin components transverse to the ma...

The power-relevant features of Raman random fiber laser (RRFL), such as lasing threshold, slope efficiency, and power distribution, are among the most critical parameters to characterize its operation status. In this work, focusing on the power features of the half-open cavity RRFL, an ultrafast convergent power-balance model is proposed, which hig...

Transient regimes, often difficult to characterize, can be fundamental in establishing final steady states features of reaction-diffusion phenomena. This is particularly true in ecological problems. Here, through both numerical simulations and an analytic approximation, we analyze the transient of a nonequilibrium superdiffusive random search when...

The interplay between gain and scattering of light propagating in disordered media allows operation of random lasers (RLs)—lasers without conventional optical cavities. In the present paper, we review our recent contributions in this area, which include the demonstration of self-second-harmonic and self-sum-frequency generation, the characterizatio...

Movement is fundamental to the animal ecology, determining how, when, and where an individual interacts with the environment. The animal dynamics is usually inferred from trajectory data described as a combination of moves and turns, which are generally influenced by the vast range of complex stochastic stimuli received by the individual as it move...

Transient regimes, often difficult to characterize, can be fundamental in establishing final steady states features of reaction-diffusion phenomena. This is particularly true in ecological problems. Here, through both numerical simulations and an analytic approximation, we analyze the transient of a nonequilibrium superdiffusive random search when...

Functional brain networks are often constructed by quantifying correlations between time series of activity of brain regions. Their topological structure includes nodes, edges, triangles, and even higher-dimensional objects. Topological data analysis (TDA) is the emerging framework to process data sets under this perspective. In parallel, topology...

The ubiquitous Lévy α-stable distributions lack general closed-form expressions in terms of elementary functions—Gaussian and Cauchy cases being notable exceptions. To better understand this 80-year-old conundrum, we study the complex analytic continuation pα(z), z∈C, of the symmetric Lévy α-stable distribution family pα(x), x∈R, parametrized by 0<...

How animals explore and acquire knowledge from the environment is a key question in movement ecology. For pollinators that feed on multiple small replenishing nectar resources, the challenge is to learn efficient foraging routes while dynamically acquiring spatial information about new resource locations. Here, we use the behavioural mapping t-Stoc...

Skewness and non-Gaussian behavior are essential features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, although the skewness has been generally linked to time-reversal symmetry breaking and vortex stretching, the form of the asymmetric heavy tails remain elusive. Here we describe the emergence of both pr...

The statistical behavior of spectral intensity fluctuations in a Raman gain random fiber laser is investigated for the first time, to the best of our knowledge. Through a fiber Fabry–Perot tunable filter, the intensity of the filtered single wavelength from random laser (RL) spectra is measured at different pump powers. The probability density func...

The ground breaking extension of the key concept of phase structure to nonequilibrium regimes was only recently achieved in Floquet systems, characterized by a time-dependent quantum Hamiltonian with a periodic driving source. However, despite the theoretical advances, only very few systems are known to display experimental Floquet phases, not one...

In fluid turbulence, intermittency is the emergence of non-Gaussian tails in the distribution of velocity increments in small space and/or time scales. Intermittence is thus expected to gradually disappear as one moves from small to large scales. Here we study the turbulent-like intermittency effect experimentally observed in the distribution of in...

We introduce a stochastic resource-based model in which the agents acquire resources from the environment. The model dynamics is described by two coupled stochastic differential equations with distinct sources of noise, one acting on the population size and the other affecting the availability of resources. Random fluctuations from the environment...

Characterizing dynamical patterns in the (physical) state space of stochastic processes can be a challenging task. From two visualization techniques, the observable-representation and k-means clustering, a unified framework to identify such structures is developed. The only information required is the system transition matrix R (a quantity that can...

Skewness and non-Gaussian behavior are key features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, the physical origin of the asymmetry and the form of the heavy tails remain elusive. Here we describe the emergence of such properties through an exactly solvable stochastic model with a hierarchy of multiple...

Coexistence of physical phenomena can occur in quite unexpected ways. Here we demonstrate the first evidence in any physical system of the coexistence in the same set of measurements of two of the most challenging phenomena in complex systems: turbulence and spin glasses. We employ a quasi-one-dimensional random fibre laser, which displays all esse...

Functional brain networks are often constructed by quantifying correlations among brain regions. Their topological structure includes nodes, edges, triangles and even higher-dimensional objects. Topological data analysis (TDA) is the emerging framework to process datasets under this perspective. Here we report the discovery of topological phase tra...

A relevant problem in the statistical and mathematical physics literature is to derive numerically accurate expressions to calculate Lévy α-stable distributions Pα(x;β). On the formal side, important exact results rely on special functions, such as Meijer-G, Fox-H and finite sums of hypergeometric functions, with only a few exceptional cases expres...

The mixed statistical regime of a Random Fiber Laser is experimentally and theoretically studied with the framework of the generalized extreme value and alpha stable distribution statistics.

We study through a reaction-diffusion algorithm the influence of landscape diversity on the efficiency of search dynamics. Remarkably, the identical optimal search strategy arises in a wide variety of environments, provided the target density is sparse and the searcher’s information is restricted to its close vicinity. Our results strongly impact t...

We report on the extreme-value statistics of output intensities in a one-dimensional cw-pumped erbium-doped random fiber laser, with a strongly scattering disordered medium consisting of randomly spaced Bragg gratings. The experimental findings from the analysis of a large number of emission spectra are well described by the Gumbel distribution bel...

Turbulence is a challenging feature common to a wide range of complex phenomena. Random fibre lasers are a special class of lasers in which the feedback arises from multiple scattering in a one-dimensional disordered cavity-less medium. Here, we report on statistical signatures of turbulence in the distribution of intensity fluctuations in a contin...

The interest in random fiber lasers (R