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 $j=3,4,\cdots ,7$ level, and on two levels $(j_1,j_2)$ with $j_1+j_2\le 6$ 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 quadropole transition strengths for vibrational and rotational bands. There were pronounced correlations in energy ratios, sharp peaks in the Alaga ratios, and fractional collectivity across all the one-level systems, as well as signatures of triaxiality. Yrast lines consistent with a deformed rotating core were common.

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• Collective levels
• Collective models
• Electromagnetic transitions
• Energy levels
• Few-body systems
• Models & methods for nuclear reactions
• Models based on symmetries
• Nuclear many-body theory
• Nuclear structure & decays
• Shell model
• Statistical phenomena & chaos