Two-stage continuation algorithms for Bloch waves of Bose-Einstein condensates in optical lattices

Computer Physics Communications

Volumn 181, Issue 10, 2010, Pages 1727-1737

  Chien, C S ^a   Chang, S L ^b   Wu, Biao ^c  

^a CHING YUN UNIVERSITY   (Taiwan)

^b SOUTHERN TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Taiwan)

^c PEKING UNIVERSITY   (China)

Author keywords

Bifurcation; Bloch bands; Bloch surfaces; Numerical continuation

Indexed keywords

BIFURCATION; BLOCH BAND; BLOCH SURFACES; BLOCH WAVES; BOSE-EINSTEIN CONDENSATES; CONSTRAINT CONDITIONS; CONTINUATION ALGORITHM; CONTINUATION PARAMETERS; EIGENSTATES; GROSS-PITAEVSKII EQUATION; IMAGINARY PARTS; NONLINEAR EIGENVALUE PROBLEM; NUMERICAL CONTINUATION; NUMERICAL RESULTS; OPTICAL LATTICES; PERIODIC BOUNDARY CONDITIONS; TWO STAGE; WAVE NUMBERS;

BIFURCATION (MATHEMATICS); BOSE-EINSTEIN CONDENSATION; CRYSTAL LATTICES; EIGENVALUES AND EIGENFUNCTIONS; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; OPTICAL MATERIALS; STATISTICAL MECHANICS; STEAM CONDENSERS;

ALGORITHMS;

EID: 77955716644     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2010.06.030     Document Type: Article

References (19)

1. M.H. Anderson, J.R. Ensher, M.R. Matthews, C.E. Wieman, and E.A. Cornell Observation of Bose-Einstein condensation in a dilute atomic vapor Science 269 1995 198
2. K.B. Davis, M.-O. Mewes, M.R. Anderws, N.J. Van Druten, D.S. Durfee, D.M. Kurn, and W. Ketterle Bose-Einstein condensation in a gas of sodium atoms Phys. Rev. Lett. 75 1995 3969
3. E.P. Gross Hydrodynamics of a superfluid condensate J. Math. Phys. 4 1963 195
4. L.P. Pitaevskii Vortex lines in an imperfect Bose gas Zh. Eksp. Teor. Fiz. 40 1961 646
5. B. Wu, and Q. Niu Superfluidity of Bose-Einstein condensate in an optical lattice: Landau-Zener tunneling and dynamical instability New J. Phys. 5 104 2003 1
6. V.I. Yukalov, E.P. Yukalova, and V.S. Bagnato Nonlinear coherent modes of trapped Bose-Einstein condensates Phys. Rev. A 66 2002 043602
7. B. Wu, and Q. Niu Nonlinear Landau-Zener tunneling Phys. Rev. A 61 2000 023402
8. B. Wu, and Q. Niu Landau and dynamical instabilities of the superflow of Bose-Einstein condensates in optical lattices Phys. Rev. A 64 2001 061603
9. D. Diakonov, L.M. Jensen, C.J. Pethick, and H. Smith Loop structure of the lowest Bloch band for a Bose-Einstein condensate Phys. Rev. A 66 2002 013604
10. E.J. Doedel AUTO97: Continuation and bifurcation software for ordinary differential equations available via: ftp://ftp.es.concordia.ca/directory/ doedel/auto
11. T.R.O. Melvin, A.R. Champneys, P.G. Kevrekidis, and J. Cuevas Radiationless traveling waves in saturable nonlinear Schrödinger lattices Phys. Rev. Lett. 97 2006 124101
12. S.-L. Chang, C.-S. Chien, and B.-W. Jeng Computing wave functions of nonlinear Schrödinger equations: a time-independent approach J. Comput. Phys. 226 2007 104 130
13. S.-L. Chang, and C.-S. Chien Adaptive continuation algorithms for computing energy levels of rotating Bose-Einstein condensates Comput. Phys. Commun. 177 2007 707 719
14. H. Schwetlick, and J. Cleve High order predictors and adaptive steplength control in path following algorithms SIAM J. Numer. A 24 1987 1382 1393
15. J.C. Bronski, L.D. Carr, B. Deconinck, and J.N. Kutz Bose-Einstein condensates in standing waves: the cubic nonlinear Schrödinger equation with a periodic potential Phys. Rev. Lett. 86 2001 1402
16. J.C. Bronski, L.D. Carr, B. Deconinck, J.N. Kutz, and K. Promislow Bose-Einstein condensates in standing waves: the cubic nonlinear Schrödinger equation with a periodic potential Phys. Rev. E 63 2001 036612
17. B. Wu, R.B. Diener, and Q. Niu Bloch waves and Bloch bands of Bose-Einstein condensates in optical lattices Phys. Rev. A 65 2002 025601
18. J. Yang, and T.I. Lakoba Accelerated imaginary time evolution methods for the computation of solitary waves Stud. Appl. Math. 120 2008 265 292
19. S.-L. Chang, H.-S. Chen, C.-S. Chien, A multigrid continuation algorithm for multiple peak solutions of the Gross-Pitaevskii equation in a periodic potential, preprint, 2010