arXiv subjects

Javier Jiménez-López

Publications and source records attributed to Javier Jiménez-López.

6 recordsLinked to original sources

arXiv2026

Quantization of Lagrangian Descriptors

We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply organize classical transport, become finite-width phase space structures under quantum fluctuations, and their overlap provides a geometric mechanism consistent with tunneling as fluctuation-induced delocalization of transport barriers. We demonstrate this approach for the Hamiltonian saddle, where path integral sampling reveals manifold broadening and barrier penetration. This establishes a geometric framework for studying phase space transport and tunneling beyond the classical regime, while also providing a natural route toward the application of LDs to field theory.

math.DS↗

arXiv2026

Trajectory arclength reveals chaos

In this paper we demonstrate that the phase space arclength of a trajectory, quantified by the time-averaged Lagrangian descriptor, is a robust and self-contained chaos indicator. By invoking Birkhoff's Ergodic Partition Theorem, we show that this scalar function distinguishes dynamical regimes via its power spectral density: for regular motion it converges to a delta function, whereas for chaotic trajectories the spectrum exhibits an inverse power-law $(1/ω)$ driven by the phenomenon of dynamical stickiness. With this approach, we avoid the computation and simulation of the variational equations and the usage of neighboring orbits, making it the simplest geometrical chaos indicator derivable from Lagrangian descriptors. Its computational efficiency enables the study of high-dimensional systems and allows the generation of large datasets of classified initial conditions, ideal for training Machine Learning models. We validate these findings using the Hénon-Heiles and the Fermi-Pasta-Ulam systems. By linking the geometrical properties of phase space to spectral analysis, this work provides the mathematical justification to establish Lagrangian descriptors as a rigorous, self-sufficient framework for the global analysis of chaos and regularity in Hamiltonian systems.

nlin.CD↗

arXiv2026

Inclusive electron-proton measurement prospects in the Electron-Ion Collider early science stage

We explore the potential for extracting proton structure functions, proton parton density functions (PDFs), and the strong coupling $α_s(M_z^2)$, using early science data from the future Electron-Ion Collider (EIC), both standalone, and in combination with HERA data. Different scenarios are considered in which samples with modest luminosity are collected at either two or three EIC beam energy configurations. The Rosenbluth separation method is used to extract the proton structure functions $F_2$ and $F_L$ from simulated data in a model-independent manner, showing that $F_L$ can be extracted significantly more precisely with three centre of mass energies than with two, whilst also obtaining $F_2$ to higher precision than has been achieved previously. The inclusion of a third beam configuration is also beneficial in the extraction of the strong coupling $α_s(M_z^2)$ that is obtainable with unprecedented experimental precision with the early EIC data. Additionally, the precision of the proton PDFs is improved when adding these data, especially for large values of Bjorken-$x$, for both two and three EIC beam energy configurations. These studies show that EIC data will already be a highly competitive probe of perturbative Quantum Chromodynamics within the first five years of data taking.

hep-ph↗

arXiv2026

A simple chaos indicator based on the Lagrangian descriptor difference of neighboring orbits

In this paper we introduce a chaos indicator derivable from Lagrangian descriptors (LDs), defined as the difference in LD values between two neighboring trajectories. This difference LD is remarkably easy to implement and interpret, offering a direct and intuitive measure of dynamical behavior. We provide a heuristic argument linking its growth to the regularity or chaoticity due to the underlying initial condition, considering the arclength-based formulation of LDs. To evaluate its effectiveness, we benchmark it against more elaborate LD-based chaos indicators and the Smaller Aligment Index (SALI) using two prototypical systems: the Hénon-Heiles system and the Chirikov Standard Map. Our results show that, despite its simplicity, the difference LD matches the accuracy of more sophisticated methods, making it a robust and accessible tool for chaos detection in dynamical systems.

nlin.CD↗

arXiv2025

Chaoticus: a parallel approach to the computation of chaos indicators

In this paper we present Chaoticus, a Python-based package for the GPU-accelerated integration of ODE systems and the computation of chaos indicators, including SALI, GALI, Lagrangian Descriptors based indicators and the Lyapunov exponent spectrum. By leveraging GPU parallelization, our package significantly reduces the computation times by several orders of magnitude compared to CPU-based approaches. This significant reduction in computing time facilitates the generation of extensive datasets, crucial for the in-depth analysis of complex dynamics in Hamiltonian systems.

nlin.CD↗

arXiv2024

Prospects for measurements of the longitudinal proton structure function $F_L$ at the Electron Ion Collider

We explore the potential for extracting the longitudinal proton structure function $F_{L}$ at the future Electron-Ion Collider (EIC) through a Rosenbluth separation method. The impacts of differing assumptions on sample sizes, systematic uncertainties and beam energy scenarios are investigated. With a sufficiently large number of centre of mass energy configurations and well-controlled systematics, the EIC will measure $F_{L}$ to an unprecedented precision, even with relatively modest luminosities. The accessible kinematic range complements both fixed target and HERA data. In the most optimistic scenarios, the EIC data will be a highly competitive direct probe of the proton gluon density.

hep-ph↗