arXiv subjects

E. P. Raposo

Publications and source records attributed to E. P. Raposo.

18 recordsLinked to original sources

arXiv2026

Lévy walkers inside spherical shells with absorbing boundaries: Towards settling the optimal Lévy walk strategy for random searches

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 non-destructive foraging). However, a mathematically rigorous demonstration of this for dimensions $D \geq 2$ is still lacking. Here we study the very closely related problem of a Lévy walker inside annuli or spherical shells with absorbing boundaries. In the limit that corresponds to the foraging with unrestricted revisits, we show that inverse square Lévy walks optimize the search. This constitutes the strongest formal result to date supporting the optimality of inverse square Lévy walks search strategies.

cond-mat.stat-mech↗

arXiv2025

Relativistic Lévy processes

We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a genuinely new class of stochastic processes--relativistic Lévy processes. Given a system, this allows identifying distinct relativistic regimes in terms of the distribution's concavity at the origin and the probability of measuring relativistic velocities. These features provide a protocol to assess the relevance of stochastic relativistic effects in actual experiments. As supporting evidence, we find agreement with previous results about heavy-ion diffusion and show that our findings are consistent with the distribution of momentum deviations observed in measurements of antiproton cooling.

cond-mat.stat-mech↗

arXiv2023

Managing rogue quantum amplitudes: a control perspective in quantum walks

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 rogue waves increases with quantum coins close to the Pauli-Z choice, regardless the disorder degree. Conversely, for coins near Pauli-X rogue events are scarce, except under weak disorder. A monotonic threshold is observed between rare- and high-probability rogue wave regimes, depending on the quantum coin. We provide a comprehensive analysis of the coin-disorder interplay to rogue wave events. Our findings shed light on the possible control of extreme quantum amplitudes through quantum coins in disordered DTQWs.

quant-ph↗

arXiv2023

Discrete-time quantum walk dispersion control through long-range correlations

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 motion with spectrum following a power-law behavior, $S(k)\sim 1/k^ν$. The power-law correlated disorder encoded in the phases of the quantum coin is shown to give rise to a wide variety of spreading patterns of the qubit states, from localized to subdiffusive, diffusive, and superdiffusive (including ballistic) behavior, depending on the relative strength of the parameters driving the correlation degree. Dispersion control is then possible in one-dimensional discrete-time quantum walks by suitably tunning the long-range correlation properties assigned to the inhomogeneous quantum coin operator.

quant-ph↗

arXiv2023

Threshold-free estimation of entropy from a Pearson matrix

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 arbitrarily remove possibly important information. Here we propose an objective procedure for directly estimating a unique entropy of a general Pearson matrix. We show that upon rescaling the Pearson matrix satisfies all necessary conditions for an analog of the von Neumann entropy to be well defined. No thresholding is required. We demonstrate the method by estimating the entropy from neuroimaging time series of the human brain under the influence of a psychedelic.

physics.data-an↗

arXiv2022

What does it take to solve the 3D Ising model? Minimal necessary conditions for a valid solution

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 dimensional model eighty years ago. Hence, there have been many attempts to find analytic expressions for the exact partition function $Z$, but all such attempts have failed due to unavoidable conceptual or mathematical obstructions. Given the importance of this simple yet paradigmatic model, here we set out clear-cut criteria for any claimed exact expression for $Z$ to be minimally plausible. Specifically, we present six necessary -- but not sufficient -- conditions that $Z$ must satisfy. These criteria will allow very quick plausibility checks of future claims. As illustrative examples, we discuss previous mistaken ``solutions,'' unveiling their shortcomings.

cond-mat.stat-mech↗

arXiv2021

Comment on "Inverse Square Lévy Walks are not Optimal Search Strategies for d $\geq$ 2" [Phys. Rev. Lett. 124, 080601 (2020)]

It is widely accepted that inverse square Lévy 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 [Nature 401, 911 (1999)]. The precise conditions for the validity of this Lévy flight foraging hypothesis (LFH) have been widely described in the literature [Phys. Life Rev. 14, 94 (2015)]. Nevertheless, three objecting claims to the LFH have been raised recently for $d \geq 2$: (i) the capture rate $η$ has linear dependence on the target density $ρ$ for all values of the Lévy index $α$; (ii) "the gain $η_{max}/η$ achieved by varying $α$ is bounded even in the limit $ρ\to 0 $" so that "tuning $α$ can only yield a marginal gain"; (iii) depending on the values of the radius of detection $a$, the restarting distance $l_c$ and the scale parameter $s$, the optimum is realized for a range of $α$ [Phys. Rev. Lett. 124, 080601 (2020)]. Here we answer each of these three criticisms in detail and show that claims (i)-(iii) do not actually invalidate the LFH. Our results and analyses restore the original result of the LFH for non-destructive foraging.

cond-mat.stat-mech↗

arXiv2019

Emergence of skewed non-Gaussian distributions of velocity increments in isotropic turbulence

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 properties through an exactly solvable stochastic model with a scale hierarchy of energy transfer rates. From a statistical superposition of a local equilibrium distribution weighted by a background density, the increments distribution is given by a novel class of skewed heavy-tailed distributions, written as a generalization of the Meijer $G$-functions. Excellent agreement in the multiscale scenario is found with numerical data of systems with different sizes and Reynolds numbers. Remarkably, the single scale limit provides poor fits to the background density, highlighting the central role of the multiscale mechanism. Our framework can be also applied to describe the challenging emergence of skewed distributions in complex systems.

physics.flu-dyn↗

arXiv2015

First-passage times in multi-scale random walks: the impact of movement scales on search efficiency

An efficient searcher needs to balance properly the tradeoff between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free Lévy search strategies. Here we study multi-scale random walks as an approximation to the scale- free case and derive the exact expressions for their mean-first passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the asymmetric regime, in which both nearby and faraway targets are available to the searcher. For this regime, we prove that the combination of only two movement scales can be enough to outperform both balistic and Lévy strategies. This two-scale strategy involves an optimal discrimination between the nearby and faraway targets, which is only possible by adjusting the range of values of the two movement scales to the typical distances between encounters. So, this optimization necessarily requires some prior information (albeit crude) about targets distances or distributions. Furthermore, we found that the incorporation of additional (three, four, ...) movement scales and its adjustment to target distances does not improve further the search efficiency. This allows us to claim that optimal random search strategies in the asymmetric regime actually arise through the informed combination of only two walk scales (related to the exploitative and the explorative scale, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through Lévy paths (or, equivalently, through a hierarchical combination of multiple scales).

cond-mat.stat-mech↗

arXiv2008

Magnetism and Electronic Correlations in Quasi-One-Dimensional Compounds

In this contribution on the celebration of the 80th birthday anniversary of Prof. Ricardo Ferreira, we present a brief survey on the magnetism of quasi-one-dimensional compounds. This has been a research area of intense activity particularly since the first experimental announcements of magnetism in organic and organometallic polymers in the mid 80s. We review experimental and theoretical achievements on the field, featuring chain systems of correlated electrons in a special AB2 unit cell structure present in inorganic and organic compounds.

cond-mat.str-el↗

arXiv2007

The origin of power-law distributions in deterministic walks: the influence of landscape geometry

We investigate the properties of a deterministic walk, whose locomotion rule is always to travel to the nearest site. Initially the sites are randomly distributed in a closed rectangular ($A/L \times L)$ landscape and, once reached, they become unavailable for future visits. As expected, the walker step lengths present characteristic scales in one ($L \to 0$) and two ($A/L \sim L$) dimensions. However, we find scale invariance for an intermediate geometry, when the landscape is a thin strip-like region. This result is induced geometrically by a dynamical trapping mechanism, leading to a power law distribution for the step lengths. The relevance of our findings in broader contexts -- of both deterministic and random walks -- is also briefly discussed.

cond-mat.dis-nn↗

arXiv2002

Delocalization in harmonic chains with long-range correlated random masses

We study the nature of collective excitations in harmonic chains with masses exhibiting long-range correlated disorder with power spectrum proportional to $1/k^α$, where $k$ is the wave-vector of the modulations on the random masses landscape. Using a transfer matrix method and exact diagonalization, we compute the localization length and participation ratio of eigenmodes within the band of allowed energies. We find extended vibrational modes in the low-energy region for $α> 1$. In order to study the time evolution of an initially localized energy input, we calculate the second moment $M_2(t)$ of the energy spatial distribution. We show that $M_2(t)$, besides being dependent of the specific initial excitation and exhibiting an anomalous diffusion for weakly correlated disorder, assumes a ballistic spread in the regime $α>1$ due to the presence of extended vibrational modes.

cond-mat.dis-nn↗

arXiv2002

Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange

We study the one-dimensional quantum Heisenberg ferromagnet with exchange couplings exhibiting long-range correlated disorder with power spectrum proportional to $1/k^α$, where $k$ is the wave-vector of the modulations on the random coupling landscape. By using renormalization group, integration of the equations of motion and exact diagonalization, we compute the spin-wave localization length and the mean-square displacement of the wave-packet. We find that, associated with the emergence of extended spin-waves in the low-energy region for $α> 1$, the wave-packet mean-square displacement changes from a long-time super-diffusive behavior for $α<1$ to a long-time ballistic behavior for $α> 1$. At the vicinity of $α=1$, the mobility edge separating the extended and localized phases is shown to scale with the degree of correlation as $E_c\propto (α-1)^{1/3}$.

cond-mat.stat-mech↗

arXiv2001

Average Time Spent by Levy Flights and Walks on an Interval with Absorbing Boundaries

We consider a Levy flyer of order alpha that starts from a point x0 on an interval [O,L] with absorbing boundaries. We find a closed-form expression for the average number of flights the flyer takes and the total length of the flights it travels before it is absorbed. These two quantities are equivalent to the mean first passage times for Levy flights and Levy walks, respectively. Using fractional differential equations with a Riesz kernel, we find exact analytical expressions for both quantities in the continuous limit. We show that numerical solutions for the discrete Levy processes converge to the continuous approximations in all cases except the case of alpha approaching 2 and the cases of x0 near absorbing boundaries. For alpha larger than 2 when the second moment of the flight length distribution exists, our result is replaced by known results of classical diffusion. We show that if x0 is placed in the vicinity of absorbing boundaries, the average total length has a minimum at alpha=1, corresponding to the Cauchy distribution. We discuss the relevance of this result to the problem of foraging, which has received recent attention in the statistical physics literature.

cond-mat.soft↗

arXiv1998

Exact Kink Solitons in the Presence of Diffusion, Dispersion, and Polynomial Nonlinearity

We describe exact kink soliton solutions to nonlinear partial differential equations in the generic form u_{t} + P(u) u_{x} + νu_{xx} + δu_{xxx} = A(u), with polynomial functions P(u) and A(u) of u=u(x,t), whose generality allows the identification with a number of relevant equations in physics. We emphasize the study of chirality of the solutions, and its relation with diffusion, dispersion, and nonlinear effects, as well as its dependence on the parity of the polynomials $P(u)$ and $A(u)$ with respect to the discrete symmetry $u\to-u$. We analyze two types of kink soliton solutions, which are also solutions to 1+1 dimensional phi^{4} and phi^{6} field theories.

solv-int↗

arXiv1998

Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media

We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de Vries-Huxley, and Korteveg-de Vries-Burgers-Huxley equations, which combine effects of diffusion, dispersion, and nonlinearity. We emphasize the chiral behavior of the travelling solutions, whose velocities are determined by the parameters that define the equation. For some appropriate choices, we show that these equations can be mapped onto equations of motion of relativistic 1+1 dimensional phi^{4} and phi^{6} field theories of real scalar fields. We also study systems of two coupled nonlinear equations of the types mentioned.

solv-int↗

arXiv1995

Influence of frustration on a d=3 diluted antiferromagnet: $Fe_{x}Zn_{1-x}F_{2}$

The influence of a frustrated bond on the magnetic properties of a d=3 uniaxial (Ising) b.c.c. diluted antiferromagnet, with emphasis in the compound $Fe_{x}Zn_{1-x}F_{2}$, is investigated by a local mean-field numerical simulation. In particular we find that the initial drop of the saturation staggered magnetization ($M_{S}$) with concentration follows a percolation-like phenomenon characterized by an exponent $β_{p}$. For the frustrated samples, however, this regime is followed by a second one identified by a ``long tail" effect such that $M_{S}$ is zero only at the percolation threshold. Our numerical data also confirms a spin-glass phase near this threshold.

cond-mat↗

arXiv1995

Ordered Phase and Field-Induced Domains in Short-Range Ising Spin Glass

Using a microscopic numerical approach suitable to describe disordered antiferromagnets, with application to $Fe_{x}Zn_{1-x}F_{2}$, it is shown that the characteristics of the spin glass phase found for $x=0.25$ is much in agreement with the scenario predicted by the scaling theory of the droplet model.

cond-mat↗