Interplay of quantization and chaotic behaviour in ring-coupled condensates

We study large rings of weakly-coupled Bose-Einstein condensates, analysing in detail their dynamics and its dependence on the system size. Since we are interested in circulating currents and their quantisation, we consider initial conditions which result in potential maximisation of such current: equal site occupation and equal phase differences between neighbouring sites. Within the Gross-Pitaevskii approximation, we show that the current is quantised (exhibits sharp delta peaks) if the phase difference takes specific discrete values in the interval (π/2, 3π/2). The peaks, however, gradually average out to zero with increasing interaction due to chaos inherent to the system of many condensates. Eventually, the quantisation ceases to occur for a macroscopic number of sites, and the circular current manifests sinusoidal behaviour readily derived from the noninteracting limit. Marking the transition to the continuous limit.