Order, Collectivity, Structured Yrast Lines, and Correlated Energies in Random Bosonic Systems

Signatures of order and collectivity appear in a broad range of one and two level boson systems. Toy systems of $N$ particles on a single $j=3,\,4\dots 7$ level, and on 2 levels $(j_1,\,j_2)$ with $j_1+j_2 \leq 6$ were studied. Surprising novel features in the yrast lines were consistent with boson condensates. Strong signatures of order and collectivity were the norm. These included the usual energy ratios and quadrupole transition strengths for vibrational and rotational bands. There were pronounced correlations in energy ratios, sharp peaks in the Alga ratios and fractional collectivity across all the 1-level systems, as well as signatures of triaxiality