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Volumn 336, Issue 2, 2015, Pages 509-579

Thomas–Fermi Approximation for Coexisting Two Component Bose–Einstein Condensates and Nonexistence of Vortices for Small Rotation

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EID: 84925488870     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-014-2281-9     Document Type: Article
Times cited : (21)

References (32)
  • 2
    • 26044442830 scopus 로고    scopus 로고
    • Giant vortex and the breakdown of strong pinning in a rotating Bose–Einstein condensate
    • Aftalion A., Alama S., Bronsard L.: Giant vortex and the breakdown of strong pinning in a rotating Bose–Einstein condensate. Arch. Ration. Mech. Anal. 178, 247–286 (2005)
    • (2005) Arch. Ration. Mech. Anal. , vol.178 , pp. 247-286
    • Aftalion, A.1    Alama, S.2    Bronsard, L.3
  • 3
    • 79551481681 scopus 로고    scopus 로고
    • Non-existence of vortices in the small density region of a condensate
    • Aftalion A., Jerrard R.L., Royo-Letelier J.: Non-existence of vortices in the small density region of a condensate. J. Funct. Anal. 260, 2387–2406 (2011)
    • (2011) J. Funct. Anal. , vol.260 , pp. 2387-2406
    • Aftalion, A.1    Jerrard, R.L.2    Royo-Letelier, J.3
  • 4
    • 80052765060 scopus 로고    scopus 로고
    • Classification of the ground states and topological defects in a rotating two-component Bose–Einstein condensate
    • Aftalion A., Mason P.: Classification of the ground states and topological defects in a rotating two-component Bose–Einstein condensate. Phys. Rev. A 84, 033611 (2011)
    • (2011) Phys. Rev. A , vol.84 , pp. 033611
    • Aftalion, A.1    Mason, P.2
  • 5
    • 84858409030 scopus 로고    scopus 로고
    • Vortex-peak interaction and lattice shape in rotating two-component Bose–Einstein condensates
    • Aftalion A., Mason P., Wei J.: Vortex-peak interaction and lattice shape in rotating two-component Bose–Einstein condensates. Phys. Rev. A 85, 033614 (2012)
    • (2012) Phys. Rev. A , vol.85 , pp. 033614
    • Aftalion, A.1    Mason, P.2    Wei, J.3
  • 6
    • 85067728401 scopus 로고    scopus 로고
    • Royo-Letelier, J.: A minimal interface problem arising from a two component Bose–Einstein condensate via Gamma-convergence
    • Aftalion, A., Royo-Letelier, J.: A minimal interface problem arising from a two component Bose–Einstein condensate via Gamma-convergence. (to appear in Calc.Var. preprint) (2013). arXiv:1304.6650
    • To appear in Calc.Var. preprint) (2013). arXiv , pp. 6650
    • Aftalion, A.1
  • 8
    • 84887848886 scopus 로고    scopus 로고
    • On compound vortices in a two-component Ginzburg–Landau functional
    • Alama S., Bronsard L., Mironescu P.: On compound vortices in a two-component Ginzburg–Landau functional. Indiana Univ. Math. J. 61, 1861–1909 (2012)
    • (2012) Indiana Univ. Math. J. , vol.61 , pp. 1861-1909
    • Alama, S.1    Bronsard, L.2    Mironescu, P.3
  • 9
    • 0000267645 scopus 로고
    • Asymptotics for the minimization of a Ginzburg–Landau functional
    • Béthuel F., Brezis H., Hélein F.: Asymptotics for the minimization of a Ginzburg–Landau functional. Calc. Var. Part. Differ. Equ. 1, 123–148 (1993)
    • (1993) Calc. Var. Part. Differ. Equ. , vol.1 , pp. 123-148
    • Béthuel, F.1    Brezis, H.2    Hélein, F.3
  • 10
    • 0003775635 scopus 로고
    • Ginzburg–Landau Vortices
    • Birkhäuser, Boston:
    • Béthuel, F., Brezis, H., Hélein, F.: Ginzburg–Landau Vortices, PNLDE, vol. 13. Birkhäuser, Boston (1994)
    • (1994) PNLDE , vol.13
    • Béthuel, F.1    Brezis, H.2    Hélein, F.3
  • 11
    • 85015471238 scopus 로고    scopus 로고
    • Further qualitative properties for elliptic equations in unbounded domains
    • Berestycki H., Caffarelli L., Nirenberg L.: Further qualitative properties for elliptic equations in unbounded domains. Ann. Scuola Norm. Sup. Pisa 25, 69–94 (1997)
    • (1997) Ann. Scuola Norm. Sup. Pisa , vol.25 , pp. 69-94
    • Berestycki, H.1    Caffarelli, L.2    Nirenberg, L.3
  • 12
    • 84874221682 scopus 로고    scopus 로고
    • On phase-separation model: asymptotics and qualitative properties
    • Berestycki H., Lin T.-C., Wei J., Zhao C.: On phase-separation model: asymptotics and qualitative properties. Arch. Ration. Mech. Anal. 208, 163–200 (2013)
    • (2013) Arch. Ration. Mech. Anal. , vol.208 , pp. 163-200
    • Berestycki, H.1    Lin, T.-C.2    Wei, J.3    Zhao, C.4
  • 13
    • 84877881696 scopus 로고    scopus 로고
    • On entire solutions of an elliptic system modeling phase separations
    • Berestycki H., Terracini S., Wang K., Wei J.: On entire solutions of an elliptic system modeling phase separations. Adv. Math. 243, 102–126 (2013)
    • (2013) Adv. Math. , vol.243 , pp. 102-126
    • Berestycki, H.1    Terracini, S.2    Wang, K.3    Wei, J.4
  • 14
    • 0000447574 scopus 로고
    • Semilinear equations in (Formula presented.) without conditions at infinity
    • Brezis H.: Semilinear equations in $${\mathbb{R}^n}$$Rnwithout conditions at infinity. Appl. Math. Optim. 12, 271–282 (1984)
    • (1984) Appl. Math. Optim. , vol.12 , pp. 271-282
    • Brezis, H.1
  • 15
    • 46149141759 scopus 로고
    • Remarks on sublinear elliptic equations
    • Brezis H., Oswald L.: Remarks on sublinear elliptic equations. Nonlinear Anal. 10, 55–64 (1986)
    • (1986) Nonlinear Anal. , vol.10 , pp. 55-64
    • Brezis, H.1    Oswald, L.2
  • 16
    • 58149361424 scopus 로고    scopus 로고
    • Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries
    • Caffarelli L.A., Lin F.-H.: Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries. J. Am. Math. Soc. 21, 847–862 (2008)
    • (2008) J. Am. Math. Soc. , vol.21 , pp. 847-862
    • Caffarelli, L.A.1    Lin, F.-H.2
  • 17
    • 13844254046 scopus 로고    scopus 로고
    • On the superlinear Lazer–McKenna conjecture
    • Dancer E.N., Yan S.: On the superlinear Lazer–McKenna conjecture. J. Differ. Equ. 210, 317–351 (2005)
    • (2005) J. Differ. Equ. , vol.210 , pp. 317-351
    • Dancer, E.N.1    Yan, S.2
  • 18
    • 84155164478 scopus 로고    scopus 로고
    • The limit equation for the Gross–Pitaevskii equations and S. Terracini’s conjecture
    • Dancer E.N., Wang K., Zhang Z.: The limit equation for the Gross–Pitaevskii equations and S. Terracini’s conjecture. J. Funct. Anal. 262, 1087–1131 (2012)
    • (2012) J. Funct. Anal. , vol.262 , pp. 1087-1131
    • Dancer, E.N.1    Wang, K.2    Zhang, Z.3
  • 20
    • 85067713244 scopus 로고    scopus 로고
    • Gallo, C.: The ground state of two coupled Gross-Pitaevskii equations in the Thomas–Fermi limit. (preprint) (2014)
    • Gallo, C.: The ground state of two coupled Gross-Pitaevskii equations in the Thomas–Fermi limit. (preprint) (2014). arXiv:1407.4974
  • 21
    • 79957872154 scopus 로고    scopus 로고
    • On the Thomas–Fermi ground state in a harmonic potential
    • Gallo C., Pelinovsky D.: On the Thomas–Fermi ground state in a harmonic potential. Asymptot. Anal. 73, 53–96 (2011)
    • (2011) Asymptot. Anal. , vol.73 , pp. 53-96
    • Gallo, C.1    Pelinovsky, D.2
  • 22
    • 84939873114 scopus 로고
    • A priori bounds for positive solutions of nonlinear elliptic equations
    • Gidas B., Spruck J.: A priori bounds for positive solutions of nonlinear elliptic equations. Commun. Part. Differ. Equ. 6, 883–901 (1981)
    • (1981) Commun. Part. Differ. Equ. , vol.6 , pp. 883-901
    • Gidas, B.1    Spruck, J.2
  • 23
    • 0019147547 scopus 로고
    • A boundary value problem associated with the second Painlevé transcendent and the Korteweg–de Vries equation
    • Hastings S.P., McLeod J.B.: A boundary value problem associated with the second Painlevé transcendent and the Korteweg–de Vries equation. Arch. Ration. Mech. Anal. 73, 31–51 (1981)
    • (1981) Arch. Ration. Mech. Anal. , vol.73 , pp. 31-51
    • Hastings, S.P.1    McLeod, J.B.2
  • 24
    • 32544460861 scopus 로고    scopus 로고
    • The critical velocity for vortex existence in a two-dimensional rotating Bose–Einstein condensate
    • Ignat R., Millot V.: The critical velocity for vortex existence in a two-dimensional rotating Bose–Einstein condensate. J. Funct. Anal. 233, 260–306 (2006)
    • (2006) J. Funct. Anal. , vol.233 , pp. 260-306
    • Ignat, R.1    Millot, V.2
  • 25
    • 33947128571 scopus 로고    scopus 로고
    • Local minimizers with vortex filaments for a Gross-Pitaevsky functional
    • Jerrard R.L.: Local minimizers with vortex filaments for a Gross-Pitaevsky functional. ESAIM Control Optim. Calc. Var. 13, 35–71 (2007)
    • (2007) ESAIM Control Optim. Calc. Var. , vol.13 , pp. 35-71
    • Jerrard, R.L.1
  • 26
    • 84858708024 scopus 로고    scopus 로고
    • Radial and bifurcating non-radial solutions for a singular perturbation problem in the case of exchange of stabilities
    • Karali G.D., Sourdis C.: Radial and bifurcating non-radial solutions for a singular perturbation problem in the case of exchange of stabilities. Ann. I. H. Poincaré-AN 29, 131–170 (2012)
    • (2012) Ann. I. H. Poincaré-AN , vol.29 , pp. 131-170
    • Karali, G.D.1    Sourdis, C.2
  • 27
    • 85067730693 scopus 로고    scopus 로고
    • The ground state of a Gross-Pitaevskii energy with general potential in the Thomas–Fermi limit
    • Karali, G.D., Sourdis, C.: The ground state of a Gross-Pitaevskii energy with general potential in the Thomas–Fermi limit (to appear in Arch. Ration. Mech. Anal) (2014). arXiv:1205.5997
    • To appear in Arch. Ration. Mech. Anal) , pp. 5997
    • Karali, G.D.1    Sourdis, C.2
  • 28
    • 0033478708 scopus 로고    scopus 로고
    • Ginzburg–Landau type energy with discontinuous constraint
    • Lassoued L., Mironescu P.: Ginzburg–Landau type energy with discontinuous constraint. J. Anal. Math. 77, 1–26 (1999)
    • (1999) J. Anal. Math. , vol.77 , pp. 1-26
    • Lassoued, L.1    Mironescu, P.2
  • 29
    • 3242710531 scopus 로고    scopus 로고
    • Solutions with boundary layer and positive peak for an elliptic Dirichlet problem
    • Li G., Yang J., Yan S.: Solutions with boundary layer and positive peak for an elliptic Dirichlet problem. Proc. R. Soc. Edinb. 134, 515–536 (2004)
    • (2004) Proc. R. Soc. Edinb. , vol.134 , pp. 515-536
    • Li, G.1    Yang, J.2    Yan, S.3
  • 30
    • 77951146882 scopus 로고    scopus 로고
    • Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition
    • Noris B., Tavares H., Terracini S., Verzini G.: Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition. Commun. Pure Appl. Math. 3 63, 267–302 (2010)
    • (2010) Commun. Pure Appl. Math. 3 , vol.63 , pp. 267-302
    • Noris, B.1    Tavares, H.2    Terracini, S.3    Verzini, G.4
  • 31
    • 0040955540 scopus 로고    scopus 로고
    • Linear and Nonlinear Aspects of Vortices. The Ginzburg–Landau Model
    • Birkhaüser, Boston:
    • Pacard, F., Rivière, T.: Linear and Nonlinear Aspects of Vortices. The Ginzburg–Landau Model, PNLDE, vol. 39. Birkhaüser, Boston (2000)
    • (2000) PNLDE , vol.39
    • Pacard, F.1    Rivière, T.2
  • 32
    • 0000540347 scopus 로고
    • Existence of solitary waves in higher dimensions
    • Strauss W.A.: Existence of solitary waves in higher dimensions. Commun. Math. Phys. 55, 149–162 (1977)
    • (1977) Commun. Math. Phys. , vol.55 , pp. 149-162
    • Strauss, W.A.1


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