arXiv subjects

David Santiago Quevedo

Publications and source records attributed to David Santiago Quevedo.

3 recordsLinked to original sources

arXiv2026

Confined kinetics and heterogeneous diffusion driven by fractional Gaussian noise: A path integral approach

Many complex systems are described by Langevin-type equations in which the noise exhibits long-range correlations and couples to the system in a state-dependent, multiplicative manner, leading to heterogeneous non-Markovian diffusion. Here, we investigate the problem of diffusion driven by fractional Gaussian noise with a general multiplicative coefficient from a path-integral perspective. Using a stationary-phase approximation, we derive a Gaussian propagator expressed in terms of the Lamperti transform of the process. In the additive limit, our results recover the path-integral representation of fractional Brownian motion based on its Riemann-Liouville formulation and establish its equivalence with the Langevin construction. We further analyze the effect of subordinating the process to a killing rate within the Feynman-Kac framework, and develop a general procedure to derive kinetic equations in terms of effective local Hamiltonians. We show that the interplay between multiplicative diffusion and confinement induces an effective drift term, leading to probability accumulation in regions of low noise amplitude.

cond-mat.stat-mech↗

arXiv2025

Active Brownian particles in power-law viscoelastic media

Many active particles are embedded in environments that exhibit viscoelastic properties. An important class of such media lacks a single characteristic relaxation timescale when subjected to a time-dependent stress. Rather, the stress response spans a broad continuum of timescales, a behavior naturally described by a scale-free, fractal-like power-law relaxation modulus. Using a generalization of the fractional Langevin equation, we investigate an active Brownian particle embedded in a power-law viscoelastic environment with translational and rotational dynamics governed by independent fractional orders. We solve the model analytically, develop a numerical scheme to validate the theoretical predictions, and provide tools that can be used in further studies. A rich variety of diffusion regimes emerges, which modify the intermediate-time behavior of the mean squared displacement. Notably, we find that the competition between translational and rotational contributions favors a superdiffusive persistence over the standard ballistic motion, and over-stretches its characteristic timescale, fundamentally altering the standard relation between persistence and propulsion in active matter.

cond-mat.soft↗

arXiv2024

Emergent time crystal from a fractional Langevin equation with white and colored noise

We study the fractional Langevin equation with fractional $α$-order and linear friction terms of a system coupled to white and colored thermal baths using both analytical and numerical methods. We find analytical expressions for the position and the mean squared displacement (MSD) of the system using the Prabhakar-Mittag-Leffler function. The MSD exhibits long-term sub-diffusive regimes $t^α$ driven by colored noise and $t^{2α-1}$ driven by white noise. When the linear friction is neglected, periodic ordered phases emerge for small fractional orders $α\lesssim 0.1$. In particular, the zero-linear friction system driven only by colored noise manifests the properties of a time crystal, with a ground state satisfying the fluctuation-dissipation theorem and a periodicity proportional to $2π$. On the other hand, the zero-linear friction system driven only by white noise displays an out-of-equilibrium time glass phase with periodicity proportional to $π$. A mixed phase with contributions from both ground and out-of-equilibrium states is encountered when the system couples to both baths. In that case, the periodicity deviates from $2π$ due to damping effects. We test all the analytical results numerically by implementing a discrete recursive expression, where the random forces of the system are modeled as the derivative of the fractional Brownian motion. A microscopic description for the system is also provided by an extension of the Caldeira-Leggett model.

cond-mat.stat-mech↗