Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random fluctuation leads to forbidden escape of particles   A great number of physical processes are described within the context of
Hamiltonian scattering. Previous studies have rather been focused on
trajectories starting outside invariant structures, since the ones starting
inside are expected to stay trapped there forever. This is true though only for
the deterministic case. We show however that, under finitely small random
fluctuations of the field, trajectories starting inside Arnold-Kolmogorov-Moser
(KAM) islands escape within finite time. The non-hyperbolic dynamics gains then
hyperbolic characteristics due to the effect of the random perturbed field. As
a consequence, trajectories which are started inside KAM curves escape with
hyperbolic-like time decay distribution, and the fractal dimension of a set of
particles that remain in the scattering region approaches that for hyperbolic
systems. We show a universal quadratic power law relating the exponential decay
to the amplitude of noise. We present a random walk model to relate this
distribution to the amplitude of noise, and investigate this phenomena with a
numerical study applying random maps.

10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ