arXiv subjects

Marcelo de Almeida Presotto

Publications and source records attributed to Marcelo de Almeida Presotto.

3 recordsLinked to original sources

arXiv2026

First-Order Transition to Chaos with Critical Slowing Down

Can the transition from integrability to chaos be discontinuous? We show that it can, and that the resulting first-order dynamical transition coexists with critical slowing down. Using an analytically tractable confined random walk and a deterministic stadium-like billiard, we find a finite jump of the stationary diffusive observable at the transition while the relaxation time diverges. Both systems display normal diffusion and the same exponent set $(α,β,z)=(0,1/2,-2)$. We trace this agreement to a common coarse-grained mechanism: diffusion in a finite accessible domain with a diffusion coefficient that vanishes quadratically with the perturbation. The results identify a discontinuous route from integrability to chaos and provide evidence for a broader universality class of first-order dynamical transitions.

nlin.CD↗

arXiv2026

First-order integrability-breaking phase transitions in dynamical systems

We investigate a discontinuous route from integrability to chaos using a confined stochastic random walk and a deterministic stadium-like billiard. In both systems, the stationary diffusive observable exhibits a finite jump at the transition: it vanishes at the unperturbed limit but approaches a finite, geometry-controlled value for arbitrarily small nonzero perturbations, providing the characteristic order-parameter signature of a first-order transition. Despite this discontinuity, the relaxation timescale diverges as the transition is approached, revealing critical slowing down. Both models exhibit normal diffusion with $β=1/2$, a perturbation-independent stationary state with $α=0$, and a crossover iteration scaling as $n_x\proptoλ^{-2}$, yielding $z=-2$, where $λ$ denotes the corresponding perturbation parameter. The common exponent set $(α,β,z)=(0,1/2,-2)$ originates from the same coarse-grained mechanism: normal diffusion within a finite accessible domain with a diffusion coefficient that vanishes quadratically at the transition. The agreement between stochastic transport and deterministic chaotic scattering provides strong evidence for a common class of discontinuous dynamical transitions and extends the statistical-mechanics description of phase transitions to integrability-breaking dynamics.

nlin.CD↗

arXiv2026

Transport and scaling analysis in the relativistic Standard map

We investigate some statistical and transport properties of the relativistic standard map. Through the Hamiltonian of a wave packet under an electric potential, we are able to obtain a relativistic version of the standard map, where there are two control parameters that rule the dynamics: K, which is the classical intensity parameter, and β, which controls the relativity. The phase space is mixed and exhibits confined local chaos for β near unity, approaching integrability. As β is diminished (entering the semi-classical regime), diffusion in the action variable begins to occur. However, the phase space loses its axial symmetry and an invariant curve appears to limit the diffusion as β gets smaller. We investigate the diffusion in the action variable as a function of the number of iterations, showing that the root mean square action grows initially and bends towards a saturation regime for long times. Scaling properties were established for this behavior as a function of β, and a perfect collapse of the curves was obtained, indicating scaling invariance. Additionally, we investigated the transport properties concerning the survival probability of initial conditions. The decay rates of the survival probability are mainly exponential, followed by power-law tails. As we vary the value of β, the escape rates become slower and also obey a scaling law in their decay.

nlin.CD↗