PapersNo Access

DYNAMICS OF VORTICES IN TWO-DIMENSIONAL BOSE–EINSTEIN CONDENSATES

SHU-MING CHANG

Department of Mathematics, Chung Cheng U., Chiayi 621, Taiwan, ROC

Search for more papers by this author

WEN-WEI LIN

Department of Mathematics, Chung Cheng U., Chiayi 621, Taiwan, ROC

Search for more papers by this author

, and

TAI-CHIA LIN

Department of Mathematics, Tsing Hua U., Hsingchu 300, Taiwan, ROC

Search for more papers by this author

https://doi.org/10.1142/S0218127402004644Cited by:5 (Source: Crossref)

Abstract

We derive the asymptotic motion equations of vortices for the time-dependent Gross–Pitaevskii equation with a harmonic trap potential. The asymptotic motion equations form a system of ordinary differential equations which can be regarded as a perturbation of the standard Kirchhoff problem. From the numerical simulation on the asymptotic motion equations, we observe that the bounded and collisionless trajectories of three vortices form chaotic, quasi 2- or quasi 3-periodic orbits. Furthermore, a new phenomenon of 1:1-topological synchronization is observed in the chaotic trajectories of two vortices.

Keywords:

References

V. S. Afraimovich, N. N. Verichev and M. I. Rabinovich, Radiophys. Quant. Electron. 29, 795 (1986). Crossref, Google Scholar
V. S. Afraimovich, Taiwanese J. Math. 3(2), 139 (1999). Crossref, Web of Science, Google Scholar
V. S. Afraimovich, W. W. Lin and N. F. Rulkov, Int. J. Bifurcation and Chaos 10(10), 2323 (2000), DOI: 10.1142/S0218127400001456. Link, Web of Science, Google Scholar
H. Aref, Phys. Fluids 22(3), 393 (1979). Crossref, Web of Science, Google Scholar
H. Aref, Ann. Rev. Fluid Mech. 15, 345 (1983). Crossref, Web of Science, Google Scholar
N. N. Bogoliubov, J. Phys. (Moscow) 11, 23 (1947). Web of Science, Google Scholar
R. Brown and L. Kocarev, Chaos 10, 344 (2000). Crossref, Web of Science, Google Scholar
X. Chen, C. M. Elliott and T. Qi, Proc. R. Soc. Edinburgh A 124, 1075 (1994). Crossref, Web of Science, Google Scholar
F. Dalfovoet al., Rev. Mod. Phys. 71, 463 (1999). Crossref, Web of Science, Google Scholar
R. J. Donnelly , Quantized Vortices in Helium II ( Cambridge University Press , Cambridge , 1991 ) . Google Scholar
D. L. Feder, C. W. Clark and B. I. Schneider, Phys. Rev. Lett. 82, 4956 (1999). Crossref, Web of Science, Google Scholar
D. L. Federet al., Phys. Rev. Lett. 86(4), 564 (2001). Crossref, Web of Science, Google Scholar
T. Frisch, Y. Pomeau and S. Rica, Phys. Rev. Lett. 69, 1644 (1992). Crossref, Web of Science, Google Scholar
V. L. Ginzburg and L. P. Pitaevskii, Sov. Phys. JETP 7, 585 (1958). Web of Science, Google Scholar
P. Hagan, SIAM J. Appl. Math. 42(4), 762 (1982). Crossref, Web of Science, Google Scholar
A. Haraux , Nonlinear evolution equations — global behavior of solutions , Lecture Notes in Mathematics 841 ( Springer-Verlag , NY , 1981 ) . Crossref, Google Scholar
R. M. Hervé and M. Hervé, Ann. Inst. Henri Poincaré 4(11), 427 (1994). Google Scholar
http://www.netlib.org/slatec . Google Scholar
C. Josserand and Y. Pomeau, Europhys. Lett. 30, 43 (1995). Crossref, Google Scholar
G. Kirchhoff, Vorlesungen über mathematische physik 1 (Teubner, Leipzig, 1883) p. 257. Google Scholar
L. D. Landau and E. M. Lifschitz , Fluid mechanics , 2nd edn. , Course of Theoretical Physics 6 ( Pergamon Press , 1989 ) . Google Scholar
F. H. Lin and J. X. Xin, Commun. Math. Phys. 200(2), 249 (1999). Crossref, Web of Science, Google Scholar
T. C. Lin, Commun. PDE 22, 619 (1997). Web of Science, Google Scholar
T. C. Lin, Electron. J. Diff. Eqs. 2000(42), 1 (2000). Google Scholar
E. Lundh and P. Ao, Phys. Rev. A 61, 063612 (2000). Crossref, Web of Science, Google Scholar
K. W. Madisonet al., Phys. Rev. Lett. 84, 806 (2000). Crossref, Web of Science, Google Scholar
M. R. Matthewset al., Phys. Rev. Lett. 83, 2498 (1999). Crossref, Web of Science, Google Scholar
J. C. Neu, Physica D 43, 385 (1990). Crossref, Web of Science, Google Scholar
P. Nozieres and D. Pines , The theory of quantum liquids , Superfluid Bose Liquids II ( Addison-Wesley , 1990 ) . Google Scholar
T. S. Parker and L. O. Chua , Practical Numerical Algorithms for Chaotic Systems ( Springer-Verlag , 1989 ) . Crossref, Google Scholar
L. M. Percora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990). Crossref, Web of Science, Google Scholar
M. G. Rosenblum, A. S. Pikovsky and J. Kurths, Phys. Rev. Lett. 76, 1804 (1996). Crossref, Web of Science, Google Scholar
M. G. Rosenblum, A. S. Pikovsky and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997). Crossref, Web of Science, Google Scholar
A. A. Svidzinsky and A. L. Fetter, Phys. Rev. A 62(6), 063617 (2000). Crossref, Web of Science, Google Scholar
L. Ting and R. Klein , Viscous vortical flows , Lecture Notes in Physics 374 ( Springer , 1991 ) . Google Scholar
E. Weinan, Physica D 77, 383 (1994). Crossref, Web of Science, Google Scholar