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On mathematical models for Bose-Einstein condensates in optical lattices. (English) Zbl 1171.82304


MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
35J10 Schrödinger operator, Schrödinger equation
35J20 Variational methods for second-order elliptic equations
82B10 Quantum equilibrium statistical mechanics (general)
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References:

[1] Abramowitz M., Applied Math Series 55, in: Handbook of Mathematical Functions (1964) · Zbl 0171.38503
[2] Aftalion A., Progress in Nonlinear Differential Equations and Their Applications 67, in: Vortices in Bose–Einstein Condensates (2006)
[3] DOI: 10.1142/S0129055X07002997 · Zbl 1119.35081
[4] DOI: 10.1016/j.anihpc.2006.11.011 · Zbl 1202.82010
[5] DOI: 10.1016/j.jfa.2006.04.027 · Zbl 1118.82004
[6] DOI: 10.1016/S0294-1449(01)00081-6 · Zbl 1011.82032
[7] DOI: 10.1142/S0219199701000457 · Zbl 1006.82040
[8] DOI: 10.1090/S0002-9947-07-04188-8 · Zbl 1132.35081
[9] DOI: 10.1103/RevModPhys.80.885
[10] Brezis H., Analyse fonctionnelle, Théorie et applications (1983)
[11] DOI: 10.1007/978-1-4612-0287-5
[12] DOI: 10.1016/0362-546X(86)90011-8 · Zbl 0593.35045
[13] DOI: 10.1063/1.2712421 · Zbl 1112.82004
[14] DOI: 10.1017/CBO9780511662195
[15] Eastham M. S. P., The Spectral Theory of Periodic Differential Equations (1973) · Zbl 0287.34016
[16] DOI: 10.1016/0003-4916(79)90191-X · Zbl 0412.34013
[17] DOI: 10.1007/BFb0078115
[18] Helffer B., Bull. Soc. Math. France 116 pp 34–
[19] DOI: 10.1007/3-540-51783-9_19
[20] DOI: 10.1016/j.jfa.2005.06.020 · Zbl 1106.58009
[21] DOI: 10.1007/s00220-006-1524-9 · Zbl 1233.82004
[22] Lieb E. H., The Mathematics of the Bose Gas and Its Condensation (2005) · Zbl 1104.82012
[23] DOI: 10.1007/s002200100533 · Zbl 0996.82010
[24] DOI: 10.1103/PhysRevA.69.043604
[25] DOI: 10.1016/0022-1236(87)90082-6 · Zbl 0662.35023
[26] DOI: 10.1017/CBO9780511755583
[27] Pitaevskii L. P., Bose–Einstein Condensation (2003)
[28] Reed M., Methods of Modern Mathematical Physics, Vol. IV: Analysis of Operators (1978) · Zbl 0401.47001
[29] DOI: 10.1016/0003-4916(84)90125-8 · Zbl 0596.35028
[30] DOI: 10.1103/PhysRevLett.96.230402
[31] DOI: 10.1103/PhysRevA.74.033615
[32] DOI: 10.1103/PhysRevLett.89.170402
[33] DOI: 10.1088/1464-4266/5/2/352
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