In this manuscript we show that a noise-activated escape phenomenon occurs in closed Hamiltonian systems. Due to the energy fluctuations generated by the noise, the isopotential curves open up and the particles can eventually escape in finite times. This drastic change in the dynamical behavior turns the bounded motion into a chaotic scattering problem. We analyze the escape dynamics by means of the average escape time, the probability basins and the average escape time distribution. We obtain that the main characteristics of the scattering are different from the case of noisy open Hamiltonian systems. In particular, the noise-enhanced trapping, which is ubiquitous in Hamiltonian systems, does not play the main role in the escapes. On the other hand, one of our main findings reveals a transition in the evolution of the average escape time insofar the noise is increased. This transition separates two different regimes characterized by different algebraic scaling laws. We provide strong numerical evidence to show that the complete destruction of the stickiness of the KAM islands is the key reason under the change in the scaling law. This research unlocks the possibility of modeling chaotic scattering problems by means of noisy closed Hamiltonian systems. For this reason, we expect potential application to several fields of physics such us celestial mechanics and astrophysics, among others.

在这份手稿中，我们展示了在封闭的哈密顿系统中会发生噪声激活的逃逸现象。由于噪声产生的能量波动，等势曲线打开，粒子最终可以在有限的时间内逃逸。动力学行为的这种剧烈变化将有界运动转变为混沌散射问题。我们通过平均逃逸时间、概率盆地和平均逃逸时间分布来分析逃逸动力学。我们得到散射的主要特征与嘈杂的开放哈密顿系统的情况不同。特别是，在哈密顿系统中无处不在的噪声增强陷阱在逃逸中并不起主要作用。另一方面，我们的主要发现之一揭示了在噪声增加的情况下平均逃逸时间演变的转变。这种转变将两种不同的制度分开，以不同的代数标度定律为特征。我们提供了强有力的数值证据表明，KAM 岛粘性的完全破坏是标度律变化的关键原因。这项研究开启了通过嘈杂的封闭哈密顿系统对混沌散射问题进行建模的可能性。出于这个原因，我们期待在多个物理领域的潜在应用，例如天体力学和天体物理学等。我们提供了强有力的数值证据表明，KAM 岛粘性的完全破坏是标度律变化的关键原因。这项研究开启了通过嘈杂的封闭哈密顿系统对混沌散射问题进行建模的可能性。出于这个原因，我们期待在多个物理领域的潜在应用，例如天体力学和天体物理学等。我们提供了强有力的数值证据表明，KAM 岛粘性的完全破坏是标度律变化的关键原因。这项研究开启了通过嘈杂的封闭哈密顿系统对混沌散射问题进行建模的可能性。出于这个原因，我们期待在多个物理领域的潜在应用，例如天体力学和天体物理学等。