arXiv subjects

Matheus S. Palmero

Publications and source records attributed to Matheus S. Palmero.

8 recordsLinked to original sources

arXiv2026

Recurrence analysis of quantum many-body dynamics

Observables of out-of-equilibrium quantum many-body systems display complex temporal behavior that encodes the underlying physical mechanisms but typically resists straightforward interpretations. We introduce recurrence analysis - a nonlinear time-series analysis framework long established for classical dynamical systems - to investigate correlated quantum many-body dynamics. Recurrence plots provide a qualitative fingerprint of simulated or experimental data, while recurrence quantification analysis extracts corresponding numerical descriptors. Applying this framework to quenches from the paramagnetic ground state in the one-dimensional transverse-field Ising model, we observe a clear progression in the recurrence plots of two-site correlations: nearly periodic patterns in the deeply ferromagnetic phase give way to multiscale temporal structures at criticality. Recurrence quantifiers further recover the critical field strength without prior knowledge of the model, establishing recurrence analysis as a versatile tool for characterizing quantum many-body dynamics, including unsupervised detection of quantum phase transitions.

quant-ph↗

arXiv2025

High Energy States of Recurrent Chaotic Trajectories in Time-Dependent Potential Well

In this numerical study, recurrence quantification analysis of chaotic trajectories is explored to detect atypical dynamical behaviour in non-linear Hamiltonian systems. An ensemble of initial conditions is evolved up to a maximum iteration time, and the recurrence rate of each orbit is computed, allowing a subset of trajectories exhibiting significantly higher recurrences than the ensemble average to be identified. These special trajectories are determined through a suitable statistical distribution, within which peak detection reveals the respective initial condition that is evolved into a highly recurrent chaotic orbit, a phenomenon known as stickiness. By applying this methodology to a model of a classical particle in a time-dependent potential well, it is demonstrated that, for specific parameter values and initial conditions, such recurrent chaotic trajectories can give rise to transient high-energy states.

nlin.CD↗

arXiv2023

Confining and escaping magnetic field lines in Tokamaks: Analysis via symplectic map

In magnetically confined plasma, it is possible to qualitatively describe the magnetic field configuration via phase spaces of suitable symplectic maps. These phase spaces are of mixed type, where chaos coexists with regular motion, and the complete understanding of the chaotic transport is a challenge that, when overcome, may provide further knowledge into the behaviour of confined fusion plasma. This work presents two numerical investigations into characteristics of mixed phase spaces which model distinct magnetic configurations in tokamaks under different perturbation regimes. The first approach relies on a recurrence-based analysis of ensembles of chaotic trajectories to detect open field lines that widely differ from the average. The second focuses on the transient dynamical behaviour of field lines before they escape the systems. These two methods provide insights into the influence of stickiness and invariant manifolds on the evolution of chaotic trajectories, improving our understanding of how these features affect the chaotic transport and diffusion properties in mixed phase spaces. These theoretical and numerical approaches may enhance our comprehension of confined plasma behaviour and plasma-wall interactions.

physics.plasm-ph↗

arXiv2021

Measure, dimension, and complexity of the transient motion in Hamiltonian systems

Hamiltonian systems that are either open, leaking, or contain holes in the phase space possess solutions that eventually escape the system's domain. The motion described by such escape orbits before crossing the escape threshold can be understood as a transient behavior. In this work, we introduce a numerical method to visually illustrate and quantify the transient motion in Hamiltonian systems based on the transient measure, a finite-time version of the natural measure. We apply this method to two physical systems: the single-null divertor tokamak, described by a symplectic map; and the Earth-Moon system, as modeled by the planar circular restricted three-body problem. Our results portray how different locations for the ensemble of initial conditions may lead to different transient dynamical scenarios in both systems. We show that these scenarios can be properly quantified from a geometrical aspect, the transient correlation dimension, and a dynamical aspect, the transient complexity coefficient.

nlin.CD↗

arXiv2020

Sub-diffusive behavior in the Standard Map

In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that the stickiness phenomena, present in the mixed phase space of the map setup, can be characterized as a Continuous Time Random Walk model and connected to the theoretical background for anomalous diffusion. Additionally, we choose a variant of the Ulam method to numerically approximate the Perron-Frobenius operator for the map, allowing us to calculate the anomalous diffusion exponent via an eigenvalue problem, compared to the solution of the Fractional Diffusion Equation. The results here corroborate other findings in the literature of anomalous transport in Hamiltonian maps and can be suitable to describe transport properties of other dynamical systems.

nlin.CD↗

arXiv2020

Controlling Escape in the Standard Map

We investigate how the diffusion exponent is affected by controlling small domains in the phase space.The main Kolomogorov-Arnold-Moser - KAM island of the Standard Map is considered to validate the investigation. The bifurcation scenario where the periodic island emits smaller resonance regions is considered and we show how closing paths escape from the island shore by controlling points and hence making the diffusion exponent smaller. We notice the bigger controlled area the smaller the diffusion exponent. We show that controlling around the hyperbolic points associated to the bifurcation is better than a random control to reduce the diffusion exponent. The recurrence plot shows us channels of escape and a control applied there reduces the diffusion exponent.

nlin.CD↗

arXiv2019

Diffusion Phenomena in a Mixed Phase Space

We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in phase space, the method of images and use of the classical diffusion equation. The method is demonstrated on the simplified Fermi-Ulam accelerator model, which has a mixed phase space with chaotic seas, invariant tori and Kolmogorov-Arnold-Moser (KAM) islands. The calculated average velocities agree well with numerical simulations and with an earlier empirical theory. The procedure can readily be extended to other systems including time-dependent billiards.

cond-mat.stat-mech↗

arXiv2015

Separation of particles leading to decay and unlimited growth of energy in a driven stadium-like billiard

A competition between decay and growth of energy in a time-dependent stadium billiard is discussed giving emphasis in the decay of energy mechanism. A critical resonance velocity is identified for causing of separation between ensembles of high and low energy and a statistical investigation is made using ensembles of initial conditions both above and below the resonance velocity. For high initial velocity, Fermi acceleration is inherent in the system. However for low initial velocity, the resonance allies with stickiness hold the particles in a regular or quasi-regular regime near the fixed points, preventing them from exhibiting Fermi acceleration. Also, a transport analysis along the velocity axis is discussed to quantify the competition of growth and decay of energy and making use distributions of histograms of frequency, and we set that the causes of the decay of energy are due to the capture of the orbits by the resonant fixed points.

nlin.CD↗