arXiv subjects

Esther D. Gutiérrez

Publications and source records attributed to Esther D. Gutiérrez.

4 recordsLinked to original sources

arXiv2026

Heterogeneous diffusion with recruitment and mortality

We study a heterogeneous diffusion process with a position-dependent diffusion coefficient in the presence of independent recruitment and mortality. This framework generalises heterogeneous diffusion under stochastic resetting, which is recovered as the special case of equal recruitment and mortality rates. At long times, the system approaches a non-equilibrium stationary state with a mean squared displacement that saturates to a value independent of the recruitment rate. Crucially, this saturation limit directly encodes the underlying transport regime via an effective exponent applied to the diffusion coefficient, and we characterise the non-trivial transition to this stationary regime. We further derive the mean first-passage time to a target and show that, for a fixed recruitment-to-mortality ratio, an optimal mortality rate minimises the search time. This "mortality-assisted search" effect is confirmed by numerical evaluation. Reinterpreting recruitment and mortality as infection and removal processes, we apply the model to epidemic spreading and show that a moderate removal rate can counter-intuitively accelerate, rather than delay, the arrival of infection at a new spatial region. Beyond epidemiology, our framework offers broad relevance to systems featuring concurrent particle creation and destruction, such as bacterial growth, tracer diffusion in reactive fluids, or cellular population dynamics in crowded environments.

cond-mat.stat-mech↗

arXiv2026

Characterization of Rocking Block Behaviors with Classical and Alternative Restitution Models

This work investigates how restitution modeling affects the dynamics of rocking blocks subjected to harmonic excitation. While several studies have reported discrepancies between experimentally observed impact behavior and the predictions obtained using the classical Housner restitution coefficient, the implications of adopting alternative restitution formulations on the global dynamics of rocking systems remain largely unexplored. The system is formulated as a hybrid non-smooth dynamical model and analyzed through bifurcation diagrams, Lyapunov exponents, and basins of attraction for different slenderness ratios. By comparing the classical restitution model proposed by Housner with the alternative formulation of Mao et al., we show that the choice of restitution model strongly influences the predicted system response. The alternative formulation leads to an earlier onset and greater prevalence of complex oscillations, as well as changes in the type, stability, and accessibility of attractors compared to the classical model. However, as the slenderness ratio increases, the dynamical features produced by both formulations progressively converge, indicating a reduced sensitivity to the restitution model for taller blocks. These results provide a dynamical perspective on why alternative restitution formulations, which predict impact responses closer to experimental observations, can produce markedly different behaviors from those obtained using the classical Housner model.

physics.optics↗

arXiv2025

Generalised fractional Rabi problem

Fractional quantum dynamics provides a natural framework to capture nonlocal temporal behavior and memory effects in quantum systems. In this work, we analyze the physical consequences of fractional-order quantum evolution using a Green's function formulation based on the Caputo fractional derivative. Explicit iterative expressions for the evolved state are derived and applied to an extended two-level Rabi model, a paradigmatic setting for coherent quantum control. We find that even in the absence of external driving, the static Hamiltonian term induces non-trivial spin dynamics with damping features directly linked to the fractional temporal nonlocality. When a periodically varying driving field is introduced, the competition between energy injection and memory effects gives rise to a richer dynamical behavior, manifest in the evolution of spin polarization, autocorrelation function, and fidelity. Unlike the standard Rabi oscillations characterized by a fixed frequency, the fractional regime introduces controllable damping and dephasing governed by the degree of fractionality. These distinctive signatures could be observable through the Loschmidt echo and autocorrelation function, and would offer potential routes to probe fractional quantum dynamics experimentally. Our findings open pathways toward exploring memory-induced dynamical phenomena in other systems effectively described by a two-level approximation, such as graphene-like materials and topological SSH chains, where non-integer order evolution may reveal novel topological or relaxation effects.

quant-ph↗

arXiv2021

Criticality and the fractal structure of -5/3 turbulent cascades

Here we show a procedure to generate an analytical structure producing a cascade that scales as the energy spectrum in isotropic homogeneous turbulence. We obtain a function that unveils a non-self-similar fractal at the origin of the cascade. It reveals that the backbone underlying $-5/3$ cascades is formed by deterministic nested polynomials with parameters tuned in a Hopf bifurcation critical point. The cascade scaling is exactly obtainable (not by numerical simulations) from deterministic low dimensional nonlinear dynamics. Consequently, it should not be exclusive for fluids but also present in other complex phenomena. The scaling is obtainable both in deterministic and stochastic situations.

physics.flu-dyn↗