TY - JOUR
T1 - Exploring bistability in rotating BoseEinstein condensates by a quotient transformation invariant continuation method
AU - Kuo, Yueh Cheng
AU - Lin, Wen Wei
AU - Shieh, Shih Feng
AU - Wang, Weichung
N1 - Funding Information:
The authors are grateful to the anonymous referees for their valuable suggestions and comments. This work is partially supported by the National Science Council of Taiwan , the National Center for Theoretical Sciences , and the Taida Institute of Mathematical Sciences .
PY - 2011/1/1
Y1 - 2011/1/1
N2 - We study the discrete nonlinear Schrdinger (DNLS) equations that model rotating BoseEinstein Condensates (BEC) both analytically and numerically. Due to the difficulties associated with transformation invariant solutions, standard continuation methods may not properly follow the solution curves of the DNLS equations. We propose a quotient transformation invariant continuation method to circumvent this obstacle. We also analyze the bifurcation properties of the primal stalk solution curve corresponding to the DNLS equations for an isotropic trap. In numerical computation, the existence of a bistable region corresponding to the bound states with a 0- or 1-vortex is shown. This finding not only agrees with the physics of the experimental phenomena, but also explains why a 0- or 1-vortex may be observed within a certain region that has an angular velocity. Numerical evidence shows that trap potentials have little effect on the width of the bistable regions. In contrast, intra-component scattering length significantly affects the bistable region.
AB - We study the discrete nonlinear Schrdinger (DNLS) equations that model rotating BoseEinstein Condensates (BEC) both analytically and numerically. Due to the difficulties associated with transformation invariant solutions, standard continuation methods may not properly follow the solution curves of the DNLS equations. We propose a quotient transformation invariant continuation method to circumvent this obstacle. We also analyze the bifurcation properties of the primal stalk solution curve corresponding to the DNLS equations for an isotropic trap. In numerical computation, the existence of a bistable region corresponding to the bound states with a 0- or 1-vortex is shown. This finding not only agrees with the physics of the experimental phenomena, but also explains why a 0- or 1-vortex may be observed within a certain region that has an angular velocity. Numerical evidence shows that trap potentials have little effect on the width of the bistable regions. In contrast, intra-component scattering length significantly affects the bistable region.
KW - Bistability
KW - Nonlinear Schrdinger equations
KW - Quotient transformation invariant continuation method
KW - Rotating BoseEinstein condensates
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U2 - 10.1016/j.physd.2010.08.008
DO - 10.1016/j.physd.2010.08.008
M3 - Article
AN - SCOPUS:78649324592
SN - 0167-2789
VL - 240
SP - 78
EP - 88
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1
ER -