Skyrmion is supposed to be topologically stable; Experimentally, it is not stable! Critical re-examination of existing theory of spinor dynamics First successful creation of Skyrmion spin texture in spinor BEC Shin group, PRL 108, 035301 (2012)
Spin-1 BEC classified as Spin-spin interaction in the spin-1 condensate: Dynamics of spin-1 BEC: Gross-Pitaevskii(GP) Equation antiferromagnetic (AFM) for g 2 > 0 ferromagnetic (FM) for g 2 <0 Where
: Initial state Implicitly assumed dynamics occur within AFM or FM manifold
Strategy: project onto three orthogonal spinors to get three hydrodynamic equations (Refael, PRB 2009)
Mass continuity eq: Euler eq: Landau-Lifshitz eq: And… No spatio-temporal fluctuation is allowed within FM manifold!! In FM Limit
No spatio-temporal fluctuation is allowed within AFM manifold with ONE EXCEPTION (next talk) Mass continuity eq: Euler eq: Landau-Lifshitz eq: In AFM Limit Again… !
All dynamics involves evolution into a mixed state (δ ≠ 0)
Relation to Skyrmion dynamics From homotopy consideration, stability of Skyrmion only guaranteed within AFM manifold. However, temporal evolution within AFM manifold is intrinsically forbidden!! Therefore, there is no meaning to Skyrmion as a topological object.
Conclusion: Initially tried to understand unstable Skyrmion dynamics Instead found neither AFM nor FM sub-manifold supports a well-define d dynamics (FM; t=0) (FM+AFM, t>0) (AFM; t=0) (AFM+FM, t>0) Numerical solution of the Gross-Pitaevskii equation proves our claim (next talk)