DOI QR코드

DOI QR Code

NOTE ON THE GROUND STATES OF TWO-COMPONENT BOSE-EINSTEIN CONDENSATES WITH AN INTERNAL ATOMIC JOSEPHSON JUNCTION

  • Received : 2011.07.11
  • Published : 2013.09.30

Abstract

In this paper, we consider two-component Bose-Einstein condensates with an internal atomic Josephson junction in the general case, i.e., 0 < p < $\frac{2}{(d-2)^+}$. We prove existence and uniqueness results for the ground states, and obtain some properties of the ground states with large parameters.

Keywords

References

  1. W. Bao, Ground states and dynamics of multicomponent Bose-Einstein condensates, Multiscale Model. Simul. 2 (2004), no. 2, 210-236. https://doi.org/10.1137/030600209
  2. W. Bao and Y. Cai, Ground states of two-component Bose-Einstein condensates with an internal atomic Josephson junction, East Asia Journal of Applied Mathematics 1 (2011), no. 1, 49-81. https://doi.org/10.4208/eajam.190310.170510a
  3. S. M. Chang, C. S. Lin, T. C. Lin, and W. W. Lin, Segregated nodal domains of two-dimensional multispecies Bose-Einstein condensates, Phys. D 196 (2004), no. 3-4, 341-361. https://doi.org/10.1016/j.physd.2004.06.002
  4. S. M. Chang, W. W. Lin, and S. F. Shieh, Gauss-Seidel-type methods for energy states of a multi-component Bose-Einstein condensate, J. Comput. Phys. 202 (2005), no. 1, 367-390. https://doi.org/10.1016/j.jcp.2004.07.012
  5. D. Jaksch, S. A. Gardiner, K. Schulze, J. I. Cirac, and P. Zoller, Uniting Bose-Einstein condensate in optical resonators, Phys. Rev. Lett. 86 (2001), no. 21, 4733-4736. https://doi.org/10.1103/PhysRevLett.86.4733
  6. E. H. Lieb, R. Seiringer, and J. Yngvason, Bosons in a trap: a rigorous derivation of the Gross-Pitaevskii energy functional, Phy. Rev. A 61 (2000), article 043602.
  7. E. H. Lieb and J. P. Solovej, Ground state energy of the two-component charged Bose gas, Comm. Math. Phys. 252 (2004), no. 1-3, 485-534. https://doi.org/10.1007/s00220-004-1144-1
  8. L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation, Clarendon Press, 2003.
  9. J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, Nonlinear Josephson-type oscillations of a driven two-component Bose-Einstein condensate, Phys. Rev. A 59 (1999), article R31-R34.
  10. Y. Zhang, W. Bao, and H. Li, Dynamics of rotating two-component Bose-Einstein con-densates and its efficient computation, Phys. D 234 (2007), no. 1, 49-69. https://doi.org/10.1016/j.physd.2007.06.026