arXiv subjects

Pedro Julián-Salgado

Publications and source records attributed to Pedro Julián-Salgado.

3 recordsLinked to original sources

arXiv2026

Mirror transitions in diffusion with stochastic resetting confined on a ring

Diffusion with an incorporated resetting mechanism provides a reference framework for modeling a wide range of natural phenomena. Within this framework, the optimal resetting rate is a key quantity that arises from the optimization of the mean first-passage time. While substantial work has focused on the study of the optimal resetting rate in unbounded one dimensional domains, little is still known about the optimization of the mean first-passage time in bounded systems, in particular when multiple resetting sites are available. In this work, we consider a particle diffusing along a circular circumference and under resetting, with an absorbing target site at a fixed location. Using the appropriate free propagator for this system, we compute the Laplace transform of the survival probability when resetting occurs to multiple sites drawn from an arbitrary probability density function. We also calculate the mean first-passage time at the target site, and study the dependence of the optimal resetting rate in terms of the relevant parameters of the system in a two-resetting site configuration. Depending on the arc length between one of the resetting sites and the absorbing target site, and the weight of the remaining resetting site, the optimal resetting rate can exhibit abrupt ("first order'') and continuous ("second order'') transitions. Moreover, the behavior of the mean first-passage time is rich enough to allow both critical and tri-critical points to exist in the parameter space. All the transitions have "mirror symmetry'' around the selected target site and its corresponding diametrically opposite site.

cond-mat.stat-mech↗

arXiv2025

Abrupt transitions in the optimization of diffusion with distributed resetting

Brownian diffusion subject to stochastic resetting to a fixed position has been widely studied for applications to random search processes. In an unbounded domain, the mean first-passage time at a target site can be minimized for a convenient choice of the resetting rate. Here we study this optimization problem in one dimension when resetting occurs to random positions, chosen from a probability density function with compact support that does not include the target. Depending on the shape of this distribution, the optimal resetting rate either varies smoothly with the mean distance to the target, as in single-site resetting, or exhibits a discontinuity caused by the presence of a second local minimum in the mean first-passage time. These two regimes are separated by a critical line containing a singular point that we characterize through a Ginzburg-Landau theory. To quantify how useful is a given resetting point for the search, we calculate the probability density function of the last resetting position before absorption. The discontinuous transition separates two markedly different optimal strategies: one with a small resetting rate where the last path before absorption starts from a rather distant but likely position, while the other strategy has a large resetting rate, favoring last paths starting from not-so-likely points but which are closer to the target.

cond-mat.stat-mech↗

arXiv2024

Diffusion with two resetting points

We study the problem of a target search by a Brownian particle subject to stochastic resetting to a pair of sites. The mean search time is minimized by an optimal resetting rate which does not vary smoothly, in contrast with the well-known single site case, but exhibits a discontinuous transition as the position of one resetting site is varied while keeping the initial position of the particle fixed, or vice-versa. The discontinuity vanishes at a "liquid-gas" critical point in position space. This critical point exists provided that the relative weight $m$ of the further site is comprised in the interval $[2.9028...,8.5603...]$. When the initial position follows the resetting point distribution, a discontinuous transition also exists for the optimal rate as the distance between the resetting points is varied, provided that $m$ exceeds the critical value $m_c=6.6008...$ This setup can be mapped onto an intermittent search problem with switching diffusion coefficients and represents a minimal model for the study of distributed resetting.

cond-mat.stat-mech↗