Spinor Bose-Einstein condensates in double well potentials
  We consider the statics and dynamics of F = 1 spinor Bose-Einstein condensates (BECs) confined in double well potentials. We use a two-mode Galerkin-type quasi-analytical approximation to describe the stationary states of the system. This way, we are able to obtain not only earlier results based on the single mode approximation (SMA) frequently used in studies of spinor BECs, but also additional modes that involve either two or all three spinor components of the F = 1 spinor BEC. The results based on this Galerkin-type decomposition are in good agreement with the analysis of the full system. We subsequently analyze the stability of these multi-component states, as well as their dynamics when we find them to be unstable. The instabilities of the symmetric or anti-symmetric states exhibit symmetry-breaking and recurrent asymmetric patterns. Our results yield qualitatively similar bifurcation diagrams both for polar (such as Na23) and ferromagnetic (such as Rb87) spinor BECs. 
C. Wang, P.G. Kevrekidis, N. Whitaker, T.J. Alexander, D.J.   Frantzeskakis and P. Schmelcher