arXiv subjects

Hernan Larralde

Publications and source records attributed to Hernan Larralde.

9 recordsLinked to original sources

arXiv2025

Extreme statistics and spacing distribution in a Brownian gas correlated by resetting

We study a one-dimensional gas of $N$ Brownian particles that diffuse independently, but are {\it simultaneously} reset to the origin at a constant rate $r$. The system approaches a non-equilibrium stationary state (NESS) with long-range interactions induced by the simultaneous resetting. Despite the presence of strong correlations, we show that several observables can be computed exactly, which include the global average density, the distribution of the position of the $k$-th rightmost particle and the spacing distribution between two successive particles. Our analytical results are confirmed by numerical simulations. We also discuss a possible experimental realisation of this resetting gas using optical traps.

cond-mat.stat-mech↗

arXiv2006

Metastability in Markov processes

We present a formalism to describe slowly decaying systems in the context of finite Markov chains obeying detailed balance. We show that phase space can be partitioned into approximately decoupled regions, in which one may introduce restricted Markov chains which are close to the original process but do not leave these regions. Within this context, we identify the conditions under which the decaying system can be considered to be in a metastable state. Furthermore, we show that such metastable states can be described in thermodynamic terms and define their free energy. This is accomplished showing that the probability distribution describing the metastable state is indeed proportional to the equilibrium distribution, as is commonly assumed. We test the formalism numerically in the case of the two-dimensional kinetic Ising model, using the Wang--Landau algorithm to show this proportionality explicitly, and confirm that the proportionality constant is as derived in the theory. Finally, we extend the formalism to situations in which a system can have several metastable states.

cond-mat.stat-mech↗

arXiv2006

Occurrence of normal and anomalous diffusion in polygonal billiard channels

From extensive numerical simulations, we find that periodic polygonal billiard channels with angles which are irrational multiples of pi generically exhibit normal diffusion (linear growth of the mean squared displacement) when they have a finite horizon, i.e. when no particle can travel arbitrarily far without colliding. For the infinite horizon case we present numerical tests showing that the mean squared displacement instead grows asymptotically as t log t. When the unit cell contains accessible parallel scatterers, however, we always find anomalous super-diffusion, i.e. power-law growth with an exponent larger than 1. This behavior cannot be accounted for quantitatively by a simple continuous-time random walk model. Instead, we argue that anomalous diffusion correlates with the existence of families of propagating periodic orbits. Finally we show that when a configuration with parallel scatterers is approached there is a crossover from normal to anomalous diffusion, with the diffusion coefficient exhibiting a power-law divergence.

cond-mat.stat-mech↗

arXiv2005

The statistics of diffusive flux

We calculate the explicit probability distribution function for the flux between sites in a simple discrete time diffusive system composed of independent random walkers. We highlight some of the features of the distribution and we discuss its relation to the local instantaneous entropy production in the system. Our results are applicable both to equilibrium and non-equilibrium steady states as well as for certain time dependent situations.

cond-mat.stat-mech↗

arXiv2005

A Definition of Metastability for Markov Processes with Detailed Balance

A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types of slowly decaying modes and which leads to properties similar to those postulated in the restricted ensemble approach \cite{pen71}. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible. As a concrete application of our formalism we present preliminary results on a 2D kinetic Ising model.

cond-mat.stat-mech↗

arXiv2003

Levy walk patterns in the foraging movements of spider monkeys (Ateles geoffroyi)

Scale invariant patterns have been found in different biological systems, in many cases resembling what physicists have found in other nonbiological systems. Here we describe the foraging patterns of free-ranging spider monkeys (Ateles geoffroyi) in the forest of the Yucatan Peninsula, Mexico and find that these patterns resemble what physicists know as Levy walks. First, the length of a trajectory s constituent steps, or continuous moves in the same direction, is best described by a power-law distribution in which the frequency of ever larger steps decreases as a negative power function of their length. The rate of this decrease is very close to that predicted by a previous analytical Levy walk model to be an optimal strategy to search for scarce resources distributed at random Viswanathan et al 1999). Second, the frequency distribution of the duration of stops or waiting times also approximates a power-law function. Finally, the mean square displacement during the monkeys first foraging trip increases more rapidly than would be expected from a random walk with constant step length, but within the range predicted for Levy walks. In view of these results, we analyze the different exponents characterizing the trajectories described by females and males, and by monkeys on their own or when part of a subgroup. We discuss the origin of these patterns and their implications for the foraging ecology of spider monkeys.

physics.bio-ph↗

arXiv2002

Translocation Properties of Primitive Molecular Machines and Their Relevance to the Structure of the Genetic Code

We address the question, related with the origin of the genetic code, of why are there three bases per codon in the translation to protein process. As a followup to our previous work, we approach this problem by considering the translocation properties of primitive molecular machines, which capture basic features of ribosomal/messenger RNA interactions, while operating under prebiotic conditions. Our model consists of a short one-dimensional chain of charged particles(rRNA antecedent) interacting with a polymer (mRNA antecedent) via electrostatic forces. The chain is subject to external forcing that causes it to move along the polymer which is fixed in a quasi one dimensional geometry. Our numerical and analytic studies of statistical properties of random chain/polymer potentials suggest that, under very general conditions, a dynamics is attained in which the chain moves along the polymer in steps of three monomers. By adjusting the model in order to consider present day genetic sequences, we show that the above property is enhanced for coding regions. Intergenic sequences display a behavior closer to the random situation. We argue that this dynamical property could be one of the underlying causes for the three base codon structure of the genetic code.

physics.bio-ph↗

arXiv2001

Transport Properties of the Diluted Lorentz Slab

We study the behavior of a point particle incident from the left on a slab of a randomly diluted triangular array of circular scatterers. Various scattering properties, such as the reflection and transmission probabilities and the scattering time are studied as a function of thickness and dilution. We show that a diffusion model satisfactorily describes the mentioned scattering properties. We also show how some of these quantities can be evaluated exactly and their agreement with numerical experiments. Our results exhibit the dependence of these scattering data on the mean free path. This dependence again shows excellent agreement with the predictions of a Brownian motion model.

cond-mat.stat-mech↗

arXiv1998

Transmission and Scattering of a Lorentz Gas on a Slab

We perform numerical scattering experiments on a Lorentz array of disks centered on a triangular lattice with L columns and study its transmission and reflection properties. In the finite horizon case, the motion of the particles may be modeled as simple one dimensional random walks with absorbing walls for which the scaling of the transmission and reflection coefficients are known, and agree with those found numerically. In the infinite horizon case the analogy with a simple diffusive process is no longer valid. In this case we compare our results with those expected for a one dimensional Levy walk, again with absorbing walls, for which logarithmic corrections to the scaling relations appear. The scaling with L and the symmetry properties of the forward and the backward are also studied, and some of their salient features are discussed.

cond-mat.stat-mech↗