Dynamical symmetry breaking through AI: The dimer self-trapping transition

Abstract: The nonlinear dimer obtained through the nonlinear Schr{\"o}dinger equation has been a workhorse for the discovery the role nonlinearity plays in strongly interacting systems. While the analysis of the stationary states demonstrates the onset of a symmetry broken state for some degree of nonlinearity, the full dynamics maps the system into an effective $\phi^4$ model. In this latter context, the self-trapping transition is an initial condition dependent transfer of a classical particle over a barrier set by the nonlinear term. This transition has been investigated analytically and mathematically it is expressed through the hyperbolic limit of Jacobian elliptic functions. The aim of the present work is to recapture this transition through the use of methods of AI. Specifically, we used a physics motivated machine learning model that is shown to be able to capture the original dynamic self-trapping transition and its dependence on initial conditions. Exploitation of this result in the case of the non-degenerate nonlinear dimer gives additional information on the more general dynamics and helps delineate linear from nonlinear localization. This work shows how AI methods may be embedded in physics and provide useful tools for discovery.