Elementary excitation families and their frequency ordering in cylindrically symmetric Bose–Einstein Condensates

We present a systematic classification of the elementary excitations of Bose–Einstein condensates in cylindrical traps in terms of their shapes. The classification generalizes the concept of families of excitations first identified by Hutchinson and Zaremba [Hutchinson D A W and Zaremba E 1998 Phys. Rev. A 57 1280]. We relate the energy ordering of the modes to their family classification, and provide a simple model which explains the relationship.