  Quantum many body systems with long range interactions are known to display
many fascinating phenomena experimentally observable in trapped ions, Rydberg
atoms and polar molecules. Among these are dynamical phase transitions which
occur after an abrupt quench in spin chains with interactions decaying as
$r^{-\alpha}$ and whose critical dynamics depend crucially on the power
$\alpha$: for systems with $\alpha<1$ the transition is sharp while for
$\alpha>1$ it fans out in a chaotic crossover region. In this paper we explore
the fate of critical dynamics in Ising chains with long-range interactions when
the transverse field is ramped up with a finite speed. While for abrupt
quenches we observe a chaotic region that widens as $\alpha$ is increased, the
width of the crossover region diminishes as the time of the ramp increases,
suggesting that chaos will disappear altogether and be replaced by a sharp
transition in the adiabatic limit.

Statistical Mechanics;Quantum Physics