  Weakly nonintegrable many-body systems can restore ergodicity in distinctive
ways depending on the range of the interaction network in action space. Action
resonances seed chaotic dynamics into the networks. Long range networks provide
well connected resonances with ergodization controlled by the individual
resonance chaos time scales. Short range networks instead yield a dramatic
slowing down of ergodization in action space, and lead to rare resonance
diffusion. We use Josephson junction chains as a paradigmatic study case. We
exploit finite time average distributions to characterize the thermalizing
dynamics of actions. We identify a novel action resonance diffusion regime
responsible for the slowing down. We extract the diffusion coefficient of that
slow process and measure its dependence on the proximity to the integrable
limit. Independent measures of correlation functions confirm our findings. The
observed fragile diffusion is relying on weakly chaotic dynamics in spatially
isolated action resonances. It can be suppressed, and ergodization delayed, by
adding weak action noise, as a proof of concept.
