arXiv subjects

Hernán Larralde

Publications and source records attributed to Hernán Larralde.

At least 19 recordsLinked to original sources

arXiv2026

Quantum backflow in biased tight-binding systems

We study the phenomenon of quantum backflow in tight-binding systems with complex couplings, considering different boundary conditions and lattice sizes. Backflow is an intrinsically non-classical effect where the density flux associated with a particle described by the superposition of wave functions with, say, positive momentum, acquires negative values. We calculate the superposition of positive momentum states that gives rise to the strongest backflow in the system. We also evaluate the bounds on the total amount of probability that flows in the opposite direction of the particle's momentum.

quant-ph↗

arXiv2025

Scaling and shape of financial returns distributions modeled as conditionally independent random variables

We show that assuming that the returns are independent when conditioned on the value of their variance (volatility), which itself varies in time randomly, then the distribution of returns is well described by the statistics of the sum of conditionally independent random variables. In particular, we show that the distribution of returns can be cast in a simple scaling form, and that its functional form is directly related to the distribution of the volatilities. This approach explains the presence of power-law tails in the returns as a direct consequence of the presence of a power law tail in the distribution of volatilities. It also provides the form of the distribution of Bitcoin returns, which behaves as a stretched exponential, as a consequence of the fact that the Bitcoin volatilities distribution is also closely described by a stretched exponential. We test our predictions with data from the S\&P 500 index, Apple and Paramount stocks; and Bitcoin.

q-fin.ST↗

arXiv2025

From anomalous diffusion in polygons to a transport locking relation

We study particle transport in a class of open channels of finite length, made of identical cells of connected open polygonal billiards with parallel boundaries. In these systems the Mean Square Displacement (MSD) grows in time faster than linearly. We show that irrespective of the geometry of these channels, the distribution of the first return times decays algebraically with two different exponents, separated by a crossover region that is determined by the MSD. We find that the distribution of first return times satisfies a simple scaling form. In turn, the transmission coefficient, defined as the fraction of trajectories that starting at the cell at the origin escape the channel through the other boundary, decays algebraically with the size of the system, and, as a signature of non-recurrent transport, sometimes slower. From these two processes we derive a locking relation among the scaling exponents for the asymptotic behavior of the MSD, the times of first return to the origin and the way transmission decays with the system size, showing that these three processes are interdependent. The locking relation holds for diffusive processes, as well as for fractional Brownian motion with arbitrary Hurst exponent. We argue that the locking relation may be valid for many other transport processes, Markovian or not, with finite MSD.

cond-mat.stat-mech↗

arXiv2024

Spectra and transport of probability and energy densities in a $\mathcal{PT}$-symmetric square well with a delta-function potential

We study the spectrum, eigenstates and transport properties of a simple $\mathcal{P}\mathcal{T}$-symmetric model consisting in a finite, complex, square well potential with a delta potential at the origin. We show that as the strength of the delta potential increases, the system exhibits exceptional points accompanied by an accumulation of density associated with the break in the $\mathcal{P}\mathcal{T}$-symmetry. We also obtain the density and energy density fluxes and analyze their transport properties. We find that in the $\mathcal{P}\mathcal{T}-$ symmetric phase transport is efficient, in the sense that all the density that flows into the system at the source, flows out at the sink, which is sufficient to derive a generalized unitary relation for the transmission and reflection coefficients.

quant-ph↗

arXiv2024

Exact extreme, order and sum statistics in a class of strongly correlated system

Even though strongly correlated systems are abundant, only a few exceptional cases admit analytical solutions. In this paper we present a large class of solvable systems with strong correlations.. We consider a set of $N$ independent and identically distributed (i.i.d) random variables $\{X_1,\, X_2,\ldots, X_N\}$ whose common distribution has a parameter $Y$ (or a set of parameters) which itself is random with its own distribution. For a fixed value of this parameter $Y$, the $X_i$ variables are independent and we call them conditionally independent and identically distributed (c.i.i.d). However, once integrated over the distribution of the parameter $Y$, the $X_i$ variables get strongly correlated, yet retaining a solvable structure for various observables, such as for the sum and the extremes of $X_i$'s. This provides a simple procedure to generate a class of solvable strongly correlated systems. We illustrate how this procedure works via three physical examples where $N$ particles on a line perform independent (i) Brownian motions, (ii) ballistic motions with random initial velocities, and (iii) Lévy flights, but they get strongly correlated via {\it simultaneous resetting} to the origin. Our results are verified in numerical simulations. This procedure can be used to generate an endless variety of solvable strongly correlated systems.

cond-mat.stat-mech↗

arXiv2023

On the energy density in quantum mechanics

There are several definitions of energy density in quantum mechanics. These yield expressions that differ locally, but all satisfy a continuity equation and integrate to the value of the expected energy of the system under consideration. Thus, the question of whether there are physical grounds to choose one definition over another arises naturally. In this work, we propose a way to probe a system by varying the size of a well containing a quantum particle. We show that the mean work done by moving the wall is closely related to one of the definitions for energy density. Specifically, the appropriate energy density, evaluated at the wall corresponds to the force exerted by the particle locally, against which the work is done. We show that this identification extends to two and three dimensional systems.

quant-ph↗

arXiv2023

Dynamical properties of volume at the spread in the Bitcoin/USD market

The study of order volumes in financial markets has shown that these display several non-trivial statistical properties. Most studies have been focused on the bulk properties of volume of incoming orders or of realized transactions rather than the dynamical aspects. The present work is a study of the dynamical properties of volume. Unlike previous works, we studied the volume available at the spread rather than the volume of incoming orders or of realized transactions. We found evidence that suggests mean reverting volume changes and strong asymmetries in the equilibrium of sell and buy orders as well as the presence of clustering.

q-fin.ST↗

arXiv2022

A machine learning model to identify corruption in México's public procurement contracts

The costs and impacts of government corruption range from impairing a country's economic growth to affecting its citizens' well-being and safety. Public contracting between government dependencies and private sector instances, referred to as public procurement, is a fertile land of opportunity for corrupt practices, generating substantial monetary losses worldwide. Thus, identifying and deterring corrupt activities between the government and the private sector is paramount. However, due to several factors, corruption in public procurement is challenging to identify and track, leading to corrupt practices going unnoticed. This paper proposes a machine learning model based on an ensemble of random forest classifiers, which we call hyper-forest, to identify and predict corrupt contracts in México's public procurement data. This method's results correctly detect most of the corrupt and non-corrupt contracts evaluated in the dataset. Furthermore, we found that the most critical predictors considered in the model are those related to the relationship between buyers and suppliers rather than those related to features of individual contracts. Also, the method proposed here is general enough to be trained with data from other countries. Overall, our work presents a tool that can help in the decision-making process to identify, predict and analyze corruption in public procurement contracts.

cs.CY↗

arXiv2022

Practices of public procurement and the risk of corrupt behavior before and after the government transition in México

Corruption has a significant impact on economic growth, democracy, and inequality. It has severe consequences at the human level are incalculable. Public procurement, where public resources are used to purchase goods or services from the private sector, are particularly susceptible to corrupt practices. However, government turnover may bring significant changes in the way public contracting is done, and thus, in the levels and types of corruption involved in public procurement. In this respect, México lived a historical government transition in 2018, with the new government promising a crackdown on corruption. In this work, we analyze data from more than 1.5 million contracts corresponding from 2013 to 2020, to study to what extent this change of government affected the characteristics of public contracting, and we try to determine whether these changes affect how corruption takes place. To do this, we propose a statistical framework to compare the characteristics of the contracting practices within each administration, separating the contracts in different classes depending on whether or not they were made with companies that have now been identified as being involved in corrupt practices. We find that while the amount of resources spent with companies that turned out to be corrupt has decreased substantially, many of the patterns followed to contract these companies were maintained, and some of those in which changes did occur, are suggestive of a larger risk of corruption.

stat.AP↗

arXiv2021

Spectra, eigenstates and transport properties of a $\mathcal{PT}$-symmetric ring

We study, analytically and numerically, a simple $\mathcal{PT}$-symmetric tight-binding ring with an onsite energy $a$ at the gain and loss sites. We show that if $a\neq 0$, the system generically exhibits an unbroken $\mathcal{PT}$-symmetric phase. We study the nature of the spectrum in terms of the singularities in the complex parameter space as well as the behavior of the eigenstates at large values of the gain and loss strength. We find that in addition to the usual exceptional points, there are "diabolical points", and inverse exceptional points at which complex eigenvalues reconvert into real eigenvalues. We also study the transport through the system. We calculate the total flux from the source to the drain, and how it splits along the branches of the ring. We find that while usually the density flows from the source to the drain, for certain eigenstates a stationary "backflow" of density from the drain to the source along one of the branches can occur. We also identify two types of singular eigenstates, i.e. states that do not depend on the strength of the gain and loss, and classify them in terms of their transport properties.

quant-ph↗

arXiv2020

Spectral and transport properties of a $\mathcal{PT}$-symmetric tight-binding chain with gain and loss

We derive a continuity equation to study transport properties in a $\mathcal{PT}$-symmetric tight-binding chain with gain and loss in symmetric configurations. This allows us to identify the density fluxes in the system, and to define a transport coefficient to characterize the efficiency of transport of each state. These quantities are studied explicitly using analytical expressions for the eigenvalues and eigenvectors of the system. We find that in states with broken $\mathcal{PT}$-symmetry, transport is inefficient, in the sense that either inflow exceeds outflow and density accumulates within the system, or outflow exceeds inflow, and the system becomes depleted. We also report the appearance of two subsets of interesting eigenstates whose eigenvalues are independent on the strength of the coupling to gain and loss. We call these opaque and transparent states. Opaque states are decoupled from the contacts and there is no transport; transparent states exhibit always efficient transport. Interestingly, the appearance of such eigenstates is connected with the divisors of the length of the system plus one and the position of the contacts. Thus the number of opaque and transparent states varies very irregularly.

quant-ph↗

arXiv2019

Universal and non-universal text statistics: Clustering coefficient for language identification

In this work we analyze statistical properties of 91 relatively small texts in 7 different languages (Spanish, English, French, German, Turkish, Russian, Icelandic) as well as texts with randomly inserted spaces. Despite the size (around 11260 different words), the well known universal statistical laws -- namely Zipf and Herdan-Heap's laws -- are confirmed, and are in close agreement with results obtained elsewhere. We also construct a word co-occurrence network of each text. While the degree distribution is again universal, we note that the distribution of Clustering Coefficients, which depend strongly on the local structure of networks, can be used to differentiate between languages, as well as to distinguish natural languages from random texts.

physics.soc-ph↗

arXiv2017

Multiple scaling behavior and nonlinear traits in music scores

We present a statistical analysis of music scores from different composers using detrended fluctuation analysis. We find different fluctuation profiles that correspond to distinct auto-correlation structures of the musical pieces. Further, we reveal evidence for the presence of nonlinear auto-correlations by estimating the detrended fluctuation analysis of the magnitude series, a result validated by a corresponding study of appropriate surrogate data. The amount and the character of nonlinear correlations vary from one composer to another. Finally, we performed a simple experiment in order to evaluate the pleasantness of the musical surrogate pieces in comparison with the original music and find that nonlinear correlations could play an important role in the aesthetic perception of a musical piece.

physics.soc-ph↗

arXiv2017

Stochastic resonance and optimal information transfer at criticality on a network model of the human connectome

Stochastic resonance is a phenomenon in which noise enhances the response of a system to an input signal. The brain is an example of a system that has to detect and transmit signals in a noisy environment, suggesting that it is a good candidate to take advantage of SR. In this work, we aim to identify the optimal levels of noise that promote signal transmission through a simple network model of the human brain. Specifically, using a dynamic model implemented on an anatomical brain network (connectome), we investigate the similarity between an input signal and a signal that has traveled across the network while the system is subject to different noise levels. We find that non-zero levels of noise enhance the similarity between the input signal and the signal that has traveled through the system. The optimal noise level is not unique; rather, there is a set of parameter values at which the information is transmitted with greater precision, this set corresponds to the parameter values that place the system in a critical regime. The multiplicity of critical points in our model allows it to adapt to different noise situations and remain at criticality.

q-bio.NC↗

arXiv2016

Ballistic annihilation with superimposed diffusion in one dimension

We consider a one-dimensional system with particles having either positive or negative velocity, which annihilate on contact. To the ballistic motion of the particle, a diffusion is superimposed. The annihilation may represent a reaction in which the two particles yield an inert species. This model has been the object of previous work, in which it was shown that the particle concentration decays faster than either the purely ballistic or the purely diffusive case. We report on previously unnoticed behaviour for large times, when only one of the two species remains and also unravel the underlying fractal structure present in the system. We also consider in detail the case in which the initial concentration of right-going particles is $1/2+\varepsilon$, with $\varepsilon\neq0$. It is shown that a remarkably rich behaviour arises, in which two crossover times are observed as $\varepsilon \to 0$.

cond-mat.stat-mech↗

arXiv2015

Three dimensional diffusion with helical persistence

We formulate the the problem of persistent diffusion in three dimensions from the perspective of the Frenet--Serret equations. In contrast to one and two dimensional systems, in three dimensions persistent diffusion is, in general, a third order process. In this paper we derive a Fokker--Planck equation for the process and we calculate its effective diffusion constant. We also provide expressions for the asymptotic average displacement of the walk, as well as explicit expressions for the Fourier--Laplace transform of the correlations between the tangent, normal and binormal vectors of the motion.

cond-mat.soft↗

arXiv2014

Temperature gradients in equilibrium: small microcanonical systems in an external field

We consider the statistical mechanics of a small gaseous system subject to a constant external field. As is well known, in the canonical ensemble the system i) obeys a barometric formula for the density profile and ii) the kinetic temperature is independent of height, even when the system is small. We show here that in the microcanonical ensemble the kinetic temperature of the particles affected by the field is not constant with height, but that rather, generally speaking, it decreases with a gradient of order 1/N. Even more, if we have a mixture of two species, one which is influenced by the field and the other which is not, we find that the two species' kinetic temperatures are generally different, even at the same height. These facts are shown in detail by studying a simple mechanical model: a Lorentz Gas where particles and spinning disks interact and the particles are subjected to a constant external force. In the microcanonical ensemble, the kinetic temperature of the particles is indeed found to vary with height; the disks' kinetic temperature, on the other hand, is height-independent, and thus, differs from that of the particles with which they interact.

cond-mat.stat-mech↗

arXiv2014

Emergence of a sustained current by coupling equilibrating systems: Making a NESS out of equilibrium

We show that coupling together two closed thermodynamic systems that independently attain equilibrium may give rise to a nonequilibrium stationary state (NESS) with a persistent, non-vanishing current. We study a simple example that is exactly soluble, consisting of random walkers with different biases towards a reflecting boundary, modelling, for example, Brownian particles with different charge states in an electric field. We obtain exact analytical expressions for the (generating functions of) concentrations and currents in the NESS for this model, and exhibit the main features by numerical simulation.

cond-mat.stat-mech↗