Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ergodic and non-ergodic many-body dynamics in strongly nonlinear
  lattices   The study of non-linear oscillator chains in classical many-body dynamics has
a storied history going back to the seminal work of Fermi, Pasta, Ulam and
Tsingou (FPUT). We introduce a new family of such systems which consist of
chains of $N$ harmonically coupled particles with the non-linearity introduced
by confining the motion of each individual particle to a box/stadium with hard
walls. The stadia are arranged on a one dimensional lattice but they
individually do not have to be one dimensional thus permitting the introduction
of chaos already at the lattice scale. For the most part we study the case
where the motion is entirely one dimensional. We find that the system exhibits
a mixed phase space for any finite value of $N$. Computations of Lyapunov
spectra at randomly picked phase space locations and a direct comparison
between Hamiltonian evolution and phase space averages indicate that the
regular regions of phase space are not significant at large system sizes. While
the continuum limit of our model is itself a singular limit of the integrable
sinh-Gordon theory, we do not see any evidence for the kind of non-ergodicity
famously seen in the FPUT work. Finally, we examine the chain with particles
confined to two dimensional stadia where the individual stadium is already
chaotic, and find a much more chaotic phase space at small system sizes.

16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
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
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys