Ergodic and nonergodic 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 Fermi, Pasta, Ulam and Tsingou (FPUT). We introduce new family such systems which consist $N$ harmonically coupled particles with non-linearity introduced by confining motion each individual particle box/stadium hard walls. stadia are arranged on one dimensional lattice but they individually do not have be thus permitting introduction chaos already at scale. For most part we case where is entirely dimensional. find that system exhibits mixed phase space for any finite value $N$. Computations Lyapunov spectra randomly picked locations direct comparison between Hamiltonian evolution averages indicate regular regions significant large sizes. While continuum limit our model itself singular integrable sinh-Gordon theory, see evidence kind non-ergodicity famously seen FPUT work. Finally, examine chain confined two stadium chaotic, much more chaotic small