Fragile Many Body Ergodicity

TL;DR

This paper investigates how the range of interactions in many-body systems influences ergodicity restoration, revealing a fragile resonance diffusion process that slows down thermalization, especially in short-range networks.

Contribution

It introduces a novel slow resonance diffusion regime in many-body systems and characterizes its dependence on interaction range and proximity to integrability.

Findings

Long-range networks facilitate faster ergodization.

Short-range networks exhibit a slow resonance diffusion regime.

Adding weak noise can suppress diffusion and delay ergodization.

Abstract

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.