Investigation of stickiness influence in the anomalous transport and diffusion for a non-dissipative Fermi–Ulam model

Abstract

We study the dynamics of an ensemble of non interacting particles constrained by two infinitely heavy walls, where one of them is moving periodically in time, while the other is fixed. The system presents mixed dynamics, where the accessible region for the particle to diffuse chaotically is bordered by an invariant spanning curve. Statistical analysis for the root mean square velocity, considering high and low velocity ensembles, leads the dynamics to the same steady state plateau for long times. A transport investigation of the dynamics via escape basins reveals that depending of the initial velocity ensemble, the decay rates of the survival probability present different shapes and bumps, in a mix of exponential, power law and stretched exponential decays. After an analysis of step-size averages, we found that the stable manifolds play the role of a preferential path for faster escape, being responsible for the bumps and different shapes of the survival probability.

An Investigation of Chaotic Diffusion in a Family of Hamiltonian Mappings Whose Angles Diverge in the Limit of Vanishingly Action

“…As discussed in Ref. [25] and also in references therein, the survival probability corresponds to the probability a particle survive along the chaotic dynamics inside a given domain without escaping such region. The survival probability, is obtained from the integration of the escape frequency histogram written as…”

“…If an ensemble of initial conditions is given above of the saturation and below of the first invariant spanning curve the scenario can be very complicated due to the existence of stickiness [25]. The relevant scaling transformations [13,16] that lead all the curves of I rms obtained from different ǫ and I 0 to overlap each other are: (i)…”

“…This procedure is repeated until the ensemble of 10 9 different phases is completely exhausted. If the phase space shows only chaos the survival probability is described by an exponential decay [25] while the existence of islands lead to local trapping, changing the exponential decay to a slower decay that might be a stretched exponential or a power law. Figure 4(a) shows a plot of the phase space for the parameter ǫ = 10 −3 and two regions delimited by the values h = 0.01 (inside the red lines) and h = 0.02 (inside the blue lines).…”