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Vortex interaction dynamics in trapped Bose-Einstein condensates

Motivated by recent experiments studying 
the dynamics of 
configurations bearing a small number of vortices in 
atomic Bose-Einstein condensates (BECs), we 
illustrate that such systems can be accurately described by 
ordinary differential equations (ODEs) incorporating the precession 
and interaction dynamics of 
vortices in 
harmonic traps. 
This dynamics is tackled in detail at the ODE level, both for 
the simpler case of equal charge vortices, 
and for the more complicated 
(yet also experimentally relevant) case of opposite charge vortices. 
In the former case, we identify the dynamics as being chiefly 
quasi-periodic (although potentially periodic), while in the 
latter, irregular dynamics may ensue 
when suitable 
external drive of the BEC cloud is also considered. Our analytical findings are 
corroborated by numerical computations of the reduced ODE system.