Vortices in Bose–Einstein condensates

Progress in Nonlinear Differential Equations and Their Application

Volumn 67, Issue , 2006, Pages 1-203

  Aftalion, Amandine ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

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EID: 84859541824     PISSN: 14211750     EISSN: 23740280     Source Type: Book Series    
DOI: None     Document Type: Chapter

References (157)

1. Abo-Shaeer JR, Raman C,Vogels JM, Ketterle W, (2001) Science 292:476.
2. Abrikosov AA, (1957) Zh. Exp. Teor. Fiz. 32:1442.
3. Aftalion A, Alama S, Bronsard L, (2005) Arch. Rat. Mech. Anal. 178:247–286.
4. Aftalion A, Blanc X, (2004) J. Math. Pures Appl. 83:765–801.
5. Aftalion A, Blanc X, (2004) preprint, to appear in SIAM Math. Anal.
6. Aftalion A, Blanc X, in preparation.
7. Aftalion A, Blanc X, Dalibard J, (2005) Phys. Rev. A 71:023611.
8. Aftalion A, Blanc X, Nier F (2005) cond-mat/0508521.
9. Aftalion A, Blanc X, Nier F (2005) preprint.
10. Aftalion A, Danaila I, (2003) Phys. Rev. A 68: 023603
11. Aftalion A, Danaila I, (2004) Phys. Rev. A 69:033608.
12. Aftalion A, Du Q, (2001) Phys. Rev. A 64:063603.
13. Aftalion A, Du Q, Pomeau Y (2003) Phys. Rev. Lett. 91:090407
14. Aftalion A, Jerrard RL, (2002) Phys. Rev. A 66:023611.
15. Aftalion A, Jerrard RL, (2003) C.R. Acad. Sci. Paris, Ser. I, 336.
16. Aftalion A, Riviere T, (2001) Phys. Rev. A 64:043611.
17. Aftalion A, Sandier E, Serfaty S, (2001) J. Math. Pures Appl. 80:339–372.
18. Albiez M, Gati R, Fölling J, Hunsmann S, Cristiani M, Oberthaler MK, (2005) Phys. Rev. Lett. 95:010402.
19. Allaire G, (1992) SIAM J. Math. Anal. 23:1482–1518.
20. Allen JF, Misener AD, (1938) Nature 141:75.
21. André N, Bauman P, Phillips D, (2003) Ann. Inst. H. Poincaré Anal. Non Linéaire 20:705–729.
22. André N, Shafrir I, (1998) Arch. Rat. Mech. Anal. 142:45–73, 75–98.
23. André N, Shafrir I, (1998) Calc. Var. PDE, 7:1–27.
24. Anglin JR, (2001) Phys. Rev. Lett. 87:240401.
25. Anglin JR, Ketterle W, (2002), Nature, 416:211–218.
26. V. Bargmann, (1961) Comm. Pure Appl. Math. 14:187–214.
27. Baym G, Pethick CJ, (2004) Phys. Rev. A, 69.
28. Berestycki H, Caffarelli L, Nirenberg L (1996) Duke Math. J. 81:467–494.
29. Berestycki H, Caffarelli L, Nirenberg L (1997) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25:69–94.
30. Berloff N, Svistunov BV, (2002) Phys. Rev. A 66:013603.
31. Berloff N, (2005) Phys. Rev. Lett. 94:120401.
32. Bethuel F, Brezis H, Helein F (1993) Calc. Var. Partial Differential Equations 1:123– 148.
33. Bethuel F, Brezis H, Helein F (1994) Ginzburg–Landau Vortices, Progress in Nonlinear Differential Equations and Their Applications, 13. Birkhäuser Boston, Cambridge, MA.
34. Bethuel F, Orlandi G, Smets D (2004) J. Eur. Math. Soc. 33:17–94.
35. Bethuel F, Rivière T, (1995) Annales IHP, Analyse non linéaire, 12: 243–303.
36. Bethuel F, Saut JC (1999) Ann. Inst. H. Poincaré Phys. Théor. 70:147–238.
37. Bleher, PM, Lebowitz JL, (1994) J. Statist. Phys. 74:167–217.
38. Bourdel T, Cubizolles J, Khaykovich L, Magalhães KMF, Kokkelmans SJJMF, Shlyapnikov GV, Salomon C, (2003), Phys. Rev. Lett. 91:020402.
39. Bourdel T, Khaykovich L, Cubizolles J, Zhang J, Chevy F, Teichmann M, Tarruell L, S Kokkelmans SJJMF, Salomon C, (2004), Phys. Rev. Lett. 93:050401.
40. Bretin V, Stock S, Seurin S, Dalibard J, (2004) Phys. Rev. Lett. 92:050403.
41. Brezis H, Merle F, Riviere T (1994) Arch. Rational Mech. Anal. 126:35–58.
42. Brezis H, Oswald L, (1986) Nonlin. Anal., vol. 10, pp. 55–64.
43. Butts D, Rokhsar R, (1999) Nature 397:327.
44. Carlen E (1991) J. Funct. Analysis 97.
45. Castin Y, Dum R, (1999) Eur. Phys. J. D, 7:399.
46. Ciarlet P, (1989) Introduction to Numerical Linear Algebra and Optimisation, Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, UK.
47. Coddington A et al., cond-mat/0405240.
48. Cohen-Tannoudji CN, in: Les Prix Nobel 1997 (The Nobel Foundation, Stockholm, 1998), pp. 87–108, Reprinted in: Rev. Mod. Phys. 70:707–719.
49. Cooper NR, Komineas S, Read N, cond-mat/0404112.
50. Cooper NR, Wilkin NK, Gunn JMF, (2001) Phys. Rev. Lett. 87, 120405.
51. Cornell EA, Wieman CE, Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments, in: Les Prix Nobel 2001 (The Nobel Foundation, Stockholm, 2002), pp. 87–108, Reprinted in: Rev. Mod. Phys. 74, 875–893;
52. Cem. Phys. Cem. 3, 476–493 (2002).
53. Crescimanno M, Koay CG, Peterson R, Walsworth R (2000) Phys. Rev. A 62:063612.
54. Dalfovo F, Giorgini S, Pitaevskii L, Stringari S, (1999) Rev. Mod. Phys. 71:463.
55. Dalfovo F, Giorgini S, Pitaevskii L, Stringari S, (1996) Phys. Rev. A 54:4213.
56. Dion CM, Cancès E, (2003) Phys. Rev. E 67:046706.
57. Dong, GC Nonlinear Partial Differential Equations of Second Order. Translated from the Chinese by Kai Seng Chou. Translations of Mathematical Monographs, 95. American Mathematical Society, Providence, RI, 1991.
58. Donnelly RJ, Quantized Vortices in Helium II, (Cambridge, 1991), Chaps. 4 and 5.
59. Engels P et al., (2003) Phys. Rev. Lett. 90: 170405–170409.
60. Feder DL, Clark CW, Schneider BI, (1999) Phys. Rev. Lett., 82:4956.
61. Feder DL, Clark CW, Schneider BI, (1999) Phys. Rev. A, 61:011601(R).
62. Fetter AL, Feder DL, Phys. Rev. A, (1998) 58:3185.
63. Fetter AL, Jackson B, and Stringari S, cond-mat/0407119.
64. Feynman RP, (1955) in Progress in Low Temperature Physics, North-Holland, Amsterdam.
65. Fischer UR, and Baym G, Phys. Rev. Lett. (2003) 90:140402.
66. Folland GB, 1989, Harmonic Analysis in Phase Space, Princeton University Press.
67. Fournais S, Helffer B, preprint 2004.
68. Frisch T, Pomeau Y, Rica S, (1992) Phys. Rev. Lett. 69:1644.
69. García-Ripoll JJ, Perez-García VM, (2001) Phys. Rev. A 63:041603(R), 64:053611.
70. Gidas B, Ni WM, Nirenberg L, (1979) Comm. Math. Phys. 68:209–243.
71. Giusti Z, (1984) Minimal Surfaces and Functions of Bounded Variations, Birkhäuser Boston, Cambridge, MA.
72. Gravejat P, private communication.
73. Gravejat P, (2003) C. R. Acad; Sci. Paris, Ser. I 336:147–152.
74. Gravejat P, (2003) Com. Math. Phys. 243:93–103.
75. Gravejat P, (2004) Ann. Inst. H. Poincaré Anal. Non Linéaire 21:591–637.
76. Gravejat P, (2005), preprint.
77. Gueron S, Shafrir I, (2000), SIAM J. Appl. Math. 60: 1–17.
78. Hall HE, Vinen WF, (1956) Proc. Roy. Soc. A 238:204.
79. Huepe C, Brachet ME, (2000) Physica D 144:20–36.
80. Ho TL, Phys. Rev. Lett. (2001) 87, 060403.
81. Ignat R, Millot V, (2005) preprint.
82. Ignat R, Millot V, (2005) preprint.
83. Jackson AD, Kavoulakis GM, Lundh E, (2004) Phys. Rev. A 69:053619.
84. Jackson B, McCann JF, Adams CS, (2000) Phys. Rev. A 61:051603.
85. Jerrard RL, (1999) SIAM J. Math. Anal., 30:721–746.
86. Jerrard RL, (2004) preprint.
87. Jerrard RL, Soner HM, (2001) Calc. Var 14:151–191.
88. Josserand C, Pomeau Y, (2001) Nonlinearity, 5:R25-R62.
89. Josserand C, Pomeau Y, (2005) Phys. Rev. A 72:023618.
90. Josserand C, Pomeau Y, Rica S, (1999) Physica D 134:111.
91. Kapitza PL (1938) Nature 141:913.
92. Kasamatsu K, Tsubota M, Ueda M, (2002) Phys. Rev. B 66:053606.
93. W. Ketterle, When atoms behave as waves: Bose-Einstein condensation and the atom laser, in: Les Prix Nobel 2001 (The Nobel Foundation, Stockholm, 2002), pp. 118–154, Reprinted in: Rev. Mod. Phys. 74, 1131–1151 (2002); Chem. Phys. Chem. 3, 736–753 (2002).
94. Kleiner WH, Roth LM, Autler SH, (1964) Phys. Rev. 133:A1226.
95. Kohn RV, Sternberg P, (1989) Proc. Royal Soc. Edin. 11A:69–84.
96. Kraemer M, Menotti M, Pitaevskii L, Stringari S, (2003) Eur. Phys. J. D 27:247.
97. Landau LD, Lifshitz EM, (1989) Mécanique des fluides, chap. 12, Mir, Moscou.
98. Lassoued L, Mironescu P, (1999) J. d’Analyse, 77:1-26.
99. Lieb E, Seiringer R, (2005) preprint.
100. Lieb E, Seiringer R, Yngvason J, (2000) Phys. Rev. A 61:0436021.
101. Lifshitz EM, Pitaevskii LP, (1980) Statistical Physics, Part 2, chap. III, Pergamon, Oxford.
102. Lin FH, Zhang P, (2005), preprint.
103. Lobo C, Sinatra A, Castin Y, (2004) Phys. Rev. Lett. 92:020403.
104. London F, (1938) Nature 141:643.
105. Lu K, Pan XB, (2000) Trans. Amer. Math. Soc. 352:1247–1276.
106. Lundh E, (2002) Phys. Rev. A 65:043604.
107. Lundh E, Pethick CJ, Smith H, (1997) Phys. Rev. A 55:2126–2131.
108. Madison K, Chevy F, Bretin V, Dalibard J, (2000) Phys. Rev. Lett.84:806.
109. Madison K, Chevy F, Wohlleben W, Dalibard J,(2000) J. Mod. Opt., 47:2715.
110. Manton N, Sutcliffe P, (2004), Topological Solitons, Cambridge University Press.
111. A. Martinez, (2002) An Introduction to Semiclassical Analysis and Microlocal Analysis. Universitext, Springer-Verlag.
112. Matthews MR et al. (1999) Phys. Rev. Lett., 83:2498.
113. Mironescu P, (1996) C. R. Acad. Sci. Paris Sér. I Math. 323:593–598.
114. Modugno M, Pricoupenko L, Castin Y, (2003) Eur. Phys. J. D 22:235–257.
115. Morse P, Ingard K, Theoretical Acoustics, McGraw-Hill, (1968).
116. Nozieres P, Pines D, The Theory of Quantum Liquids, Addison-Wesley, Redwood City, CA (1990).
117. Olshanii M, (1998) Phys. Rev. Lett 81:938–941.
118. Onofrio R, Raman C, Vogels JM, Abo-Shaeer JR, Chikkatur AP, Ketterle W, (2000) Phys. Rev. Lett. 85:2228–2231.
119. Onsager L, (1949) Nuovo Cimento 6:249.
120. Packard RE, Sanders TM, (1972) Phys. Rev. A 6:797.
121. Pethick CJ, Smith H, (2002) Bose Einstein Condensation in Dilute Gases, Cambridge University Press, Cambridge, UK.
122. Petrov DS, Salomon C, Shlyapnikov GV, (2005) Phys. Rev. A 71:012708.
123. Pines D, Nozieres P, (1966) The Theory of Quantum Liquids, Benjamin, New York.
124. Pismen LM, (1999) Vortices in Nonlinear Fields, International series of monographs on physics, 100, Oxford Science Publications.
125. Pitaevskii L, Stringari S, (2003) Bose Einstein Condensation, International series of monographs on physics, 116, Oxford Science Publications.
126. Pomeau Y, (1994) Remarques sur les écoulements incompressibles in les grands systèmes des sciences et de la technologie, eds JL Lions, J Horowitz, Masson.
127. Pricoupenko L, Castin Y, (2004) Phys. Rev. A 69: 051601(R).
128. Raman C, Abo-Shaeer JR, Vogels JM, Xu K, Ketterle W, (2001) Phys. Rev. Lett. 87:210402.
129. Raman C, Köhl M, Onofrio R, Durfee DS, Kuklewicz CE, Hadzibabic Z, Ketterle W, (1999) Phys. Rev. Lett. 83:2502–2505.
130. Raman C, Onofrio R, Vogels JM, Abo-Shaeer JR, Ketterle W, (2001) J. Low Temp. Phys. 122:99–116.
131. Reichel W in Elliptic and parabolic problems, (Pont-à-Mousson, 1994), 164–182, Pit-man Res. Notes Math. Ser., 325, Longman Sci. Tech., Harlow, 1995.
132. Riviere T, (1996) COCV 1:77.
133. Rosenbuch P, Bretin V, Dalibard J, (2002) Phys. Rev. Lett. 89:200403.
134. Sandier E, J. Functional Analysis, (1998), 152:379–403.
135. Sandier E, Serfaty S, (2000) Annales IHP, Analyse Non Linéaire 17:119–145. 135.
136. e série, 33:561–592.
137. Sandier E, Serfaty S, (2003) Calc. Var. Partial Differential Equations 17:17–28.
138. Sandier E, Serfaty S, (2004) J. Funct. Anal. 211:219–244.
139. Sandier E, Serfaty S, Magnetic Ginzburg Landau Vortices, Birkhäuser Boston, to appear.
140. Sandier E, Soret M, Potential Analysis, vol. 13 (2000), pp. 169–184.
141. Schnee K, Yngvason J, (2004) preprint.
142. V. Schweikhard, I. Coddington, P. Engels, V. P. Mogendorff, and E. A. Cornell, (2004) Phys. Rev. Lett. 92:040404.
143. Seiringer R, (2003) J. Phys. A: Math. Gen. 36, 9755–9778.
144. Serfaty S, (1999) Comm. Contemporary Mathematics, 1, No. 2: 213–254, 295–333.
145. Serfaty S, (2001) ESAIM: Control, Optim. Calc. Var., vol. 6, pp. 201–238.
146. Serrin J, (1971) Arch. Rational Mech. Anal. 43:304–318.
147. Shiffman M, (1952) J. Rational Mech. Anal. 1:605–652.
148. Sheehy DE, Radzihovsky L, (2004) cond-mat/0406205.
149. Sinova J, Hanna CB, MacDonald AH, (2002) Phys. Rev. Lett. 89:030403.
150. Stießberger JS, Zwerger W (2000) Phys. Rev. A 62:061601.
151. Stock S, Bretin V, Chevy F, Dalibard J, (2004) Europhys. Lett. 65:594.
152. Svidzinsky AA, Fetter AL, (2000) Phys. Rev. Lett., 84:5919.
153. Svidzinsky AA, Fetter AL, (2000) Phys. Rev. A, 62:63617.
154. Walser R, Williams J, Cooper J, Holland M, (1999) Phys. Rev. A 59:3878–3889.
155. Watanabe G, Baym G, Pethick CJ, (2004) Phys. Rev. Lett. 93:190401–190405.
156. Winiecki T, Jackson B, McCann JF, Adams CS (2000) J. Phys. B: At. Mol. Opt. Phys. 33:4069–4078.
157. Zaremba E, Nikuni T, Griffin A, (1999) J. of Low Temperature Physics, 116:277–345.