Ground-state solution of Bose-Einstein condensate by directly minimizing the energy functional

Journal of Computational Physics

Volumn 187, Issue 1, 2003, Pages 230-254

  Bao, Weizhu ^a   Tang, Weijun ^a,b  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^b INSTITUTE OF APPLIED PHYSICS AND COMPUTATIONAL MATHEMATICS   (China)

Author keywords

Bose Einstein condensation; Energy functional; Finite element approximation; Gross Pitaevskii equation; Ground state solution; Thomas Fermi approximation

Indexed keywords

EQUATIONS OF STATE; FINITE ELEMENT METHOD; GROUND STATE; NUMERICAL METHODS; STATISTICAL MECHANICS; TEMPERATURE;

BOSE-EINSTEIN CONDENSATES; BOSE-EINSTEIN-CONDENSATION; CYLINDRICAL SYMMETRY; ENERGY FUNCTIONALS; FINITE ELEMENT APPROXIMATIONS; GROSS-PITAEVSKII EQUATION; GROUND STATE SOLUTIONS; RADIAL SYMMETRYS; SPHERICAL SYMMETRY; THOMAS-FERMI APPROXIMATION;

BOSE-EINSTEIN CONDENSATION;

EID: 0037406449     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00097-4     Document Type: Article

References (39)

1. R.A. Adams, Sobol1ev Spaces, 1975.
2. S.K. Adhikari, Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms, Phys. Lett. A 265 (2000) 91.
3. S.K. Adhikari, Numerically study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions, Phys. Rev. E 62 (2000) 2937.
4. S.K. Adhikari, Collapse of attractive Bose-Einstein condensed vortex states in a cylindrical trap, Phys. Rev. E 65 (2002) 016703.
5. S.K. Adhikari, P. Muruganandam, Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation, J. Phys. B 35 (2002) 2831.
6. A. Aftalion, Q. Du, Vortices in a rotating Bose-Einstein condensate: critical angular velocities and energy diagrams in the Thomas-Fermi regime, Phys. Rev. A 64 (2001) 063603.
7. M.H. Anderson, J.R. Ensher, M.R. Mathews, C.E. Wieman, E.A. Cornell, Science 269 (1995) 198.
8. J.R. Anglin, W. Ketterle, Bose-Einstein condensation of atomic gases, Nature 416 (2002) 211.
9. W. Bao, D. Jaksch, P.A. Markowich, Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation, J. Comput. Phys. (to appear).
10. W. Bao, Shi Jin, P.A. Markowich, On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime, J. Comput. Phys. 175 (2002) 487.
11. W. Bao, Shi Jin, P.A. Markowich, Numerical study of time-splitting spectral discretizations of nonlinear Schrödinger equations in the semi-classical regimes, SIAM J. Sci. Comput. (to appear).
12. S.N. Bose, Z. Phys. 26 (1924) 178.
13. C.C. Bradley, C.A. Sackett, R.G. Hulet, Phys. Rev. Lett. 78 (1997) 985.
14. M.M. Cerimele, M.L. Chiofalo, F. Pistella, S. Succi, M.P. Tosi, Numerical solution of the Gross-Pitaevskii equation using an explicit finite-difference scheme: an application to trapped Bose-Einstein condensates, Phys. Rev. E 62 (2000) 1382.
15. M.M. Cerimele, F. Pistella, S. Succi, Particle-inspired scheme for the Gross-Pitaevski equation: an application to Bose-Einstein condensation, Comput. Phys. Commun. 129 (2000) 82.
16. M.L. Chiofalo, S. Succi, M.P. Tosi, Ground state of trapped interacting Bose-Einstein condensates by an explicit imaginary-time algorithm, Phys. Rev. E 62 (2000) 7438.
17. P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
18. E. Cornell, Very cold indeed: The nanokelvin physics of Bose-Einstein condensation, J. Res. Natl. Inst. Stan. 101 (1996) 419.
19. F. Dalfovo, S. Stringari, Bosons in anisotropic traps: ground state and vortices, Phys. Rev. A 53 (1996) 2477.
20. R.J. Dodd, Approximate solutions of the nonlinear Schrödinger equation for ground and excited states of Bose-Einstein condensates, J. Res. Natl. Inst. Stan. 101 (1996) 545.
21. M. Edwards, K. Burnett, Numerical solution of the nonlinear Schrödinger equation for small samples of trapped neutral atoms, Phys. Rev. A 51 (1995) 1382.
22. A. Einstein, Sitz. Ber. Kgl. Preuss. Adad. Wiss. 22 (1924) 261.
23. J.R. Ensher, D.S. Jin, M.R. Mathews, C.E. Wieman, E.A. Cornell, Phys. Rev. Lett. 77 (1996) 4984.
24. A. Gammal, T. Frederico, L. Tomio, Improved numerical approach for the time-independent Gross-Pitaevskii nonlinear Schrödinger equation, Phys. Rev. E 60 (1999) 2421.
25. A. Griffin, D. Snoke, S. Stringaro (Eds.), Bose-Einstein Condensation, Cambridge University Press, New York, 1995.
26. D. Gottlieb, S.A. Orszag, Numerical Analysis of Spectral Methods, Society for Industrial and Applied Mathematics, Philadephia, 1977.
27. E.P. Gross, Nuovo. Cimento. 20 (1961) 454.
28. M.J. Holland, D.S. Jin, M.L. Chiofalo, J. Cooper, Emergence of interaction effects in Bose-Einstein condensation, Phys. Rev. Lett. 78 (1997) 3801.
29. A.D. Jackson, G.M. Kavoulakis, C.J. Pethick, Solitary waves in clouds of Bose-Einstein condensed atoms, Phys. Rev. A 58 (1998) 2417.
30. L. Landau, E. Lifschitz, Quantum Mechanics: Non-Relativistic Theory, Pergamon Press, New York, 1977.
31. P. Leboeuf, N. Pavloff, Phys. Rev. A 64 (2001) 033602;
32. V. Dunjko, V. Lorent, M. Olshanii, Phys. Rev. Lett. 86 (2001) 5413.
33. E.H. Lieb, R. Seiringer, J. Yngvason, Bosons in a trap: a rigorous derivation of the Gross-Pitaevskii energy functional, Phys. Rev. A 61 (2000) 3602.
34. I.N. Levine, Quantum Chemistry, fifth ed., Prentice-Hall, New York, 1991.
35. K.W. Morton, D.F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, Cambridge, 1994.
36. S.G. Nash, A. Sofer, Linear and Nonlinear Programming, McGraw-Hill, New York, 1996.
37. L.P. Pitaevskii, Zh. Eksp. Teor. Fiz. 40 (1961) 646. (Sov. Phys. JETP 13 (1961) 451.)
38. P.A. Ruprecht, M.J. Holland, K. Burrett, M. Edwards, Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms, Phys. Rev. A 51 (1995) 4704.
39. B.I. Schneider, D.L. Feder, Numerical approach to the ground and excited states of a Bose-Einstein condensated gas confined in a completely anisotropic trap, Phys. Rev. A 59 (1999) 2232.