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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 (1998 Phys. Rev. A 57 1280) by introducing a second classification number that allows all possible modes to be assigned to a family. We relate the energy ordering of the modes to their family classification, and provide a simple model which explains the relationship.