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Macroscopic excitations in confined Bose-Einstein condensates, searching for quantum turbulence

We present a survey of macroscopic excitations of harmonically confined Bose-Einstein condensates (BEC), described by Gross-Pitaevskii (GP) equation, in search of routes to develop quantum turbulence. These excitations can all be created by phase imprinting techniques on an otherwise equilibrium Bose-Einstein condensate. We analyze two crossed vortices, two parallel anti-vortices, a vortex ring, a vortex with topological charge Q = 2, and a tangle of 4 vortices. Since GP equation is time-reversal invariant, we are careful to distinguish time intervals in which this symmetry is preserved and those in which rounding errors play a role. We find that the system tends to reach stationary states that may be widely classified as having either an array of vortices with collective excitations at different length scales or an agitated state composed mainly of Bogoliubov phonons.