Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 78-88 |
| Number of pages | 11 |
| Journal | Physica D: Nonlinear Phenomena |
| Volume | 240 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2011 Jan 1 |
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Keywords
- Bistability
- Nonlinear Schrdinger equations
- Quotient transformation invariant continuation method
- Rotating BoseEinstein condensates
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics
Cite this
Exploring bistability in rotating BoseEinstein condensates by a quotient transformation invariant continuation method. / Kuo, Yueh Cheng; Lin, Wen Wei; Shieh, Shih-Feng; Wang, Weichung.
In: Physica D: Nonlinear Phenomena, Vol. 240, No. 1, 01.01.2011, p. 78-88.Research output: Contribution to journal › Article
}
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
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
UR - http://www.scopus.com/inward/record.url?scp=78649324592&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78649324592&partnerID=8YFLogxK
U2 - 10.1016/j.physd.2010.08.008
DO - 10.1016/j.physd.2010.08.008
M3 - Article
AN - SCOPUS:78649324592
VL - 240
SP - 78
EP - 88
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 1
ER -