arXiv subjects

Francisco J. Sevilla

Publications and source records attributed to Francisco J. Sevilla.

At least 19 recordsLinked to original sources

arXiv2026

Nonequilibrium statistics of harmonically trapped run-and-tumble particles: An exact convolution approach

We study one-dimensional run-and-tumble particles confined by a harmonic potential and coupled to an equilibrium thermal bath. Exploiting the coupling of active and thermal degrees of freedom through the Ornstein-Uhlenbeck propagator, we show that the position distribution factorizes, as a convolution, into the Ornstein-Uhlenbeck distribution and the distribution of the athermal run-and-tumble problem. This yields closed-form results, correcting expressions from earlier treatments by identifying the Ornstein-Uhlenbeck propagator, rather than the free-diffusion one, as the correct kernel. Results are confirmed both in Fourier space and by direct Langevin simulation. We further focus our analysis on the stationary regime, characterized by two dimensionless parameters--the ratio of trapping to persistence length, and the ratio of thermal to active diffusion--which control the crossover from a non-Gaussian, boundary-peaked distribution to the Gaussian, equilibrium-like limit. Energy fluctuations and the Kullback-Leibler divergence from the equilibrium distribution quantify the resulting non-equilibrium character of the confined active particle.

cond-mat.stat-mech↗

arXiv2026

Incidence-based random walks on simplicial complexes

We introduce an incidence-based random walk on the edges of a random two-dimensional simplicial complex with a complete $1$-skeleton and independently retained triangular faces. The dynamics combine two transport channels, one mediated by vertices and the other by triangular faces, through an effective transition operator controlled by a mixing parameter $q$. This construction isolates the effects of higher-order connectivity without modifying the underlying pairwise support of the walk. We characterize the model through structural observables, spectral relaxation, stationary localization, and first-passage transport. Our results show that partial face retention generates heterogeneous higher-order connectivity, giving rise to a pronounced transport bottleneck at intermediate face densities. In this regime, the second-largest eigenvalue modulus, the inverse participation ratio of the stationary distribution, and the mean first-passage time all exhibit non-monotonic behavior, reaching their largest values at intermediate face densities. The corresponding first-passage-time distributions reveal an enhanced probability of unusually long trajectories. Together, these results establish a simple framework for investigating how heterogeneous higher-order connectivity reshapes spectral and transport properties beyond pairwise network dynamics.

cond-mat.stat-mech↗

arXiv2025

Speed of evolution in qutrit systems

The speed of evolution between perfectly distinguishable states is thoroughly analyzed in a closed three-level (qutrit) quantum system. Considering an evolution under an arbitrary time-independent Hamiltonian, we fully characterize the relevant parameters according to whether the corresponding quantum speed limit is given by the Mandelstam-Tamm, the Margolus-Levitin, or the Ness-Alberti-Sagi (dual) bound, thereby elucidating their hierarchy and relative importance. We revisit the necessary and sufficient conditions that guarantee the evolution of the initial state towards an orthogonal one in a finite time, and pay special attention to the full characterization of the speed of evolution, offering a speed map in parameter space that highlights regions associated with faster or slower dynamics. The general analysis is applied to concrete physical settings, particularly a pair of bosons governed by an extended Bose-Hubbard Hamiltonian, and a single particle in a triple-well potential. Our findings provide a framework to explore how the energetic resources and the initial configurations shape the pace of the dynamics in higher-dimensional systems.

quant-ph↗

arXiv2025

Run-and-tumble dynamics with non-reciprocal transitions between three velocity states

We investigate the transport properties of active particles undergoing a three-state run-and-tumble dynamics in one dimension, induced by non-reciprocal transition rates between self-propelling velocity states $\{-v, 0, +v\}$ that explicitly break microscopic reversibility. Departing from conventional reciprocal models, our formulation introduces a minimal yet rich framework for studying non-equilibrium transport driven by internal state asymmetries. Using kinetic Monte Carlo simulations and analytical methods, we characterize the particle's transport properties across the transition-rates space. The model exhibits a variety of non-equilibrium behaviors, including ballistic transport, giant diffusion, and Gaussian or non-Gaussian transients, depending on the degree of asymmetry in the transition rates. We identify a manifold in transition-rate space where long-time diffusive behavior emerges despite the absence of microscopic reversibility. Exact expressions are obtained for the drift, effective diffusion coefficient, and moments of the position distribution. Our results establish how internal-state irreversibility governs macroscopic transport, providing a tractable framework to study non-equilibrium active motion beyond reciprocal dynamics.

cond-mat.stat-mech↗

arXiv2024

Anomalous diffusion of scaled Brownian tracers

A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that active bath transfer to the tracer, thus the model proposed in here extends active Brownian motion, for which the stochastic dynamics of the orientation of the propelling force is described by scale Brownian motion (sBm), identified by a the time dependent diffusivity of the form $D_β\propto t^{β-1}$, $β>0$. If $β\neq1$, sBm is highly non-stationary and suitable to describe such a non-equilibrium dynamics induced by complex media. In this paper we provide analytical calculations and computer simulations to show that genuine anomalous diffusion emerge in the long-time regime, with a time scaling of the mean square displacement $t^{2-β}$, while ballistic transport $t^2$, characteristic of persistent motion, is found in the short-time one. An analysis of the time dependence of the kurtosis, and intermediate scattering function of the positions distribution, as well as the propulsion auto-correlation function, which defines the effective persistence time, are provided.

cond-mat.stat-mech↗

arXiv2024

Fractional and scaled Brownian motion on the sphere: The effects of long-time correlations on navigation strategies

We analyze \emph{fractional Brownian motion} and \emph{scaled Brownian motion} on the two-dimensional sphere $\mathbb{S}^{2}$. We find that the intrinsic long time correlations that characterize fractional Brownian motion collude with the specific dynamics (\emph{navigation strategies}) carried out on the surface giving rise to rich transport properties. We focus our study on two classes of navigation strategies: one induced by a specific set of coordinates chosen for $\mathbb{S}^2$ (we have chosen the spherical ones in the present analysis), for which we find that contrary to what occurs in the absence of such long-time correlations, \emph{non-equilibrium stationary distributions} are attained. These results resemble those reported in confined flat spaces in one and two dimensions [Guggenberger {\it et al.} New J. Phys. 21 022002 (2019), Vojta {\it et al.} Phys. Rev. E 102, 032108 (2020)], however in the case analyzed here, there are no boundaries that affects the motion on the sphere. In contrast, when the navigation strategy chosen corresponds to a frame of reference moving with the particle (a Frenet-Serret reference system), then the \emph{equilibrium} \emph{distribution} on the sphere is recovered in the long-time limit. For both navigation strategies, the relaxation times towards the stationary distribution depend on the particular value of the Hurst parameter. We also show that on $\mathbb{S}^{2}$, scaled Brownian motion, distinguished by a time-dependent diffusion coefficient with a power-scaling, is independent of the navigation strategy finding a good agreement between the analytical calculations obtained from the solution of a time-dependent diffusion equation on $\mathbb{S}^{2}$, and the numerical results obtained from our numerical method to generate ensemble of trajectories.

cond-mat.stat-mech↗

arXiv2023

Anomalous diffusion of self-propelled particles

The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an arbitrary active motion pattern modelled by a scattering function that defines the dynamics of the change of the self-propulsion direction. The exact probability density of the particle positions at a given time is obtained. From it, the time dependence of the moments, i.e., the mean square displacement and the kurtosis for an arbitrary scattering function, are derived and analysed. Anomalous diffusion is found with a crossover of the scaling exponent from $2α$ in the short-time regime to $α$ in the long-time one, $0<α<1$ being the order of the fractional derivative considered. It is shown that the exact solution found satisfies a fractional diffusion equation that accounts for the non-local and retarded effects of the Laplacian of the probability density function through a coupled temporal and spatial memory function. Such a memory function holds the complete information of the active motion pattern. In the long-time regime, space and time are decoupled in the memory function, and the time fractional telegrapher's equation is recovered. Our results are widely applicable in systems ranging from biological microorganisms to artificially designed self-propelled micrometer particles.

cond-mat.stat-mech↗

arXiv2022

Dynamics of closed quantum systems under stochastic resetting

We consider a closed quantum system subject to a stochastic resetting process. The generic expression for the resulting density operator is formulated for arbitrary resetting dynamics, fully characterised by the distribution of times between consecutive reset events. We analyse the behaviour of the state in the long-time regime, as well as the evolution of relevant quantities in the study of quantum coherence and closed- vs open-system dynamics. Our general results are complemented with examples involving paradigmatic resetting distributions, and special attention is paid to the two-level (qubit) system, in which we elucidate the effects of the renewal process on the speed of evolution toward an orthogonal state, and gain insight into the resetting applied to open systems.

quant-ph↗

arXiv2022

Dynamics of mode entanglement induced by particle-tunneling in the extended Bose-Hubbard dimer model

The evolution of mode entanglement is analysed for a system of two indistinguishable bosons with two accessible modes. Whereas entanglement remains stationary whenever the number of bosons in each mode is left invariant, it exhibits a rich dynamics under the effects of single- and two-particle tunneling. By analysing such effects in paradigmatic families of states, our results provide guidance for the design and control of specific dynamics of mode entanglement, by varying the tunneling transition rates and the preparation of the initial state.

quant-ph↗

arXiv2021

Generalized persistence dynamics for active motion

We analyze the statistical physics of self-propelled particles from a general theoretical framework that properly describes the most salient characteristic of active motion, $persistence$, in arbitrary spatial dimensions. Such a framework allows the development of a Smoluchowski-like equation for the probability density of finding a particle at a given position and time, without assuming an explicit orientational dynamics of the self-propelling velocity as Langevin-like equation-based models do. Also, the Brownian motion due to thermal fluctuations and the active one due to a general intrinsic persistent motion of the particle are taken into consideration on an equal footing. The persistence of motion is introduced in our formalism in the form of a \emph{two-time memory function}, $K(t,t^{\prime})$. We focus on the consequences when $K(t,t^{\prime})\sim (t/t^{\prime})^{-η}\exp[-Γ(t-t^{\prime})]$, $Γ$ being the characteristic persistence time, and show that it precisely describes a variety of active motion patterns characterized by $η$. We find analytical expressions for the experimentally obtainable intermediate scattering function, the time dependence of the mean-squared displacement, and the kurtosis.

cond-mat.stat-mech↗

arXiv2021

A Geometrical Method for the Smoluchowski Equation on the Sphere

A study of the diffusion of a passive Brownian particle on the surface of a sphere and subject to the effects of an external potential, coupled linearly to the probability density of the particle's position, is presented through a numerical algorithm devised to simulate the trajectories of an ensemble of Brownian particles. The algorithm is based on elementary geometry and practically only algebraic operations are used, which makes the algorithm efficient and simple, and converges, in the \textit{weak sense}, to the solutions of the Smoluchowski equation on the sphere. Our findings show that the global effects of curvature are taken into account in both the time dependent and stationary processes.

cond-mat.stat-mech↗

arXiv2021

The underlying order induced by orthogonality and the quantum speed limit

We perform a comprehensive analysis of the set of parameters $\{r_{i}\}$ that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time $τ$, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between $τ$ and the energy spectrum and allowing the classification of $\{r_{i}\}$ into families organized in a 2-simplex, $δ^{2}$. Furthermore, the states determined by $\{r_{i}\}$ are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those $r_{i}$s in $δ^{2}$ correspondent to states whose orthogonality time is limited by the Mandelstam--Tamm bound from those restricted by the Margolus--Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality.

quant-ph↗

arXiv2021

A new route toward orthogonality

We revisit the problem of determining conditions under which a pure state, that evolves under an arbitrary unitary transformation, reaches an orthogonal state in a finite amount of the transformation parameter. Simple geometric considerations disclose the existence of a fundamental limit for the minimal amount required, providing, in particular, an intuitive hint of the Mandelstam-Tamm bound. The geometric considerations leads us to focus on a particular, yet relevant, family of states that evolve towards orthogonality. Several dynamical features are discussed, which include the (relative) entropy production during transformation, and special attention is paid to multipartite systems of $N$ bosons that are allowed to tunnel between two sites. The effects of the tunneling in the amount of transformation required for the system to attain an orthogonal state are revealed, and the relation between the latter, the tunneling intensity and the mode-entanglement is explored.

quant-ph↗

arXiv2020

Two-dimensional active motion

The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of scattered angles of the swimming direction, which encompasses the pattern of motion of particles that move at constant speed. An exact analytical expression for the marginal probability density of finding a particle on a given position at a given instant, independently of its direction of motion, is provided; and a connection with a generalized diffusion equation is unveiled. Exact analytical expressions for the time dependence of the mean-square displacement and of the kurtosis of the distribution of the particle positions are presented. For this, it is shown that only the first trigonometric moments of the distribution of the scattered direction of motion are needed. The effects of persistence and of circular motion are discussed for different families of distributions of the scattered direction of motion.

cond-mat.stat-mech↗

arXiv2020

Active particles with fractional rotational Brownian motion

We study the two-dimensional overdamped motion of an active particle whose orientational dynamics is subject to fractional Brownian noise, whereas its position is affected by self-propulsion and Brownian fluctuations. From a Langevin-like model of active motion with constant swimming speed, we derive the corresponding Fokker-Planck equation, from which we find the angular probability density of the particle orientation for arbitrary values of the Hurst exponent that characterizes the fractional rotational noise. We provide analytical expressions for the velocity autocorrelation function and the translational mean-squared displacement, which show that active diffusion effectively emerges in the long-time limit for all values of the Hurst exponent. The corresponding expressions for the active diffusion coefficient and the effective rotational diffusion time are also derived. Our results are compared with numerical simulations of active particles with rotational motion driven by fractional Brownian noise, with which we find an excellent agreement.

cond-mat.stat-mech↗

arXiv2019

Predator-prey dynamics: Chasing by stochastic resetting

We analyze predator-prey dynamics in one dimension in which a Brownian predator adopts a chasing strategy that consists in stochastically resetting its current position to locations previously visited by a diffusive prey. We study three different chasing strategies, namely, active, uniform and passive which lead to different diffusive behaviors of the predator in the absence of capture. When capture is considered, regardless of the chasing strategy, the mean first-encounter time is finite and decreases with the resetting rate. This model illustrates how the use of cues significantly improves the efficiency of random searches. We compare numerical simulations with analytical calculations and find excellent agreement.

cond-mat.dis-nn↗

arXiv2019

Generalized Ornstein-Uhlenbeck Model for Active Motion

We investigate a one-dimensional model of active motion, which takes into account the effects of persistent self-propulsion through a memory function in a dissipative-like term of the generalized Langevin equation for particle swimming velocity. The proposed model is a generalization of the active Ornstein-Uhlenbeck model introduced by G. Szamel [Phys. Rev. E {\bf 90}, 012111 (2014)]. We focus on two different kinds of memory which arise in many natural systems: an exponential decay and a power law, supplemented with additive colored noise. We provide analytical expressions for the velocity autocorrelation function and the mean-squared displacement, which are in excellent agreement with numerical simulations. For both models, damped oscillatory solutions emerge due to the competition between the memory of the system and the persistence of velocity fluctuations. In particular, for a power-law model with fractional Brownian noise, we show that long-time active subdiffusion occurs with increasing long-term memory.

cond-mat.stat-mech↗

arXiv2019

Stationary superstatistics distributions of trapped run-and-tumble particles

We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential, that emerges when trapped active motion is mapped to trapped passive Brownian motion in a fictitious inhomogeneous thermal bath. We elaborate on the meaning of the non-Boltzmann-Gibbs stationary distributions that emerge as a consequence of the persistent motion of active particles. These stationary distributions are interpreted as a class of distributions in nonequilibrium statistical mechanics known as superstatistics. Our analysis provides an original insight on the link between the intrinsic nonequilibrium nature of active motion and the well-known concept of local equilibrium used in nonequilibrium statistical mechanics, and contributes to the understanding of the validity of the concept of effective temperature. Particular cases of interest, regarding specific trapping potentials used in other theoretical or experimental studies, are discussed. We point out as an unprecedented effect, the emergence of new modes of the stationary distribution as a consequence of the coupling of persistent motion in a trapping potential that varies highly enough with position.

cond-mat.stat-mech↗