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Volumn 9, Issue 8, 2008, Pages 1503-1574

Mean field limit for bosons and infinite dimensional phase-space analysis

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EID: 57349165265     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-008-0393-5     Document Type: Article
Times cited : (117)

References (46)
  • 1
    • 0035331348 scopus 로고    scopus 로고
    • Calcul pseudodifferentiel en grande dimension
    • L. Amour, P. Kerdelhué, J. Nourrigat, Calcul pseudodifferentiel en grande dimension, Asymptot. Anal. 26 (2001), no. 2, 135161.
    • (2001) Asymptot. Anal , vol.26 , Issue.2 , pp. 135161
    • Amour, L.1    Kerdelhué, P.2    Nourrigat, J.3
  • 2
    • 33644882745 scopus 로고    scopus 로고
    • From repeated to continuous quantum interactions
    • S. Attal, Y. Pautrat, From repeated to continuous quantum interactions, Ann. Henri Poincaré 7 (2006), no. 1, 59104.
    • (2006) Ann. Henri Poincaré , vol.7 , Issue.1 , pp. 59104
    • Attal, S.1    Pautrat, Y.2
  • 3
    • 0003876935 scopus 로고
    • Introduction to algebraic and constructive quantum field theory
    • Princeton University Press, Princeton, NJ
    • J. C. Baez, I. E. Segal, Z. F. Zhou, Introduction to algebraic and constructive quantum field theory, Princeton Series in Physics. Princeton University Press, Princeton, NJ, 1992.
    • (1992) Princeton Series in Physics
    • Baez, J.C.1    Segal, I.E.2    Zhou, Z.F.3
  • 4
    • 3543031680 scopus 로고    scopus 로고
    • Accuracy of the time-dependent Hartree-Fock approximation for uncorrelated initial states
    • C. Bardos, F. Golse, A. Gottlieb, N. J. Mauser, Accuracy of the time-dependent Hartree-Fock approximation for uncorrelated initial states, J. Statist. Phys. 115 (2004), no. 3-4, 1037-1055.
    • (2004) J. Statist. Phys , vol.115 , Issue.3-4 , pp. 1037-1055
    • Bardos, C.1    Golse, F.2    Gottlieb, A.3    Mauser, N.J.4
  • 6
    • 0004168768 scopus 로고
    • The Schrödinger equation, Mathematics and its applications
    • Kluwer Academic Publishers Group, Dordrecht
    • F. A. Berezin, M. A. Shubin, The Schrödinger equation, Mathematics and its applications (Soviet Series) 66, Kluwer Academic Publishers Group, Dordrecht, 1991.
    • (1991) Soviet Series , pp. 66
    • Berezin, F.A.1    Shubin, M.A.2
  • 7
    • 0003126597 scopus 로고
    • Espaces fonctionnels associés au calcul de Weyl-Hörmander
    • J. M. Bony, J. Y. Chemin, Espaces fonctionnels associés au calcul de Weyl-Hörmander, Bull. Soc. Math. France 122 (1994), no. 1, p. 77-118.
    • (1994) Bull. Soc. Math. France , vol.122 , Issue.1 , pp. 77-118
    • Bony, J.M.1    Chemin, J.Y.2
  • 8
    • 57349119162 scopus 로고    scopus 로고
    • e série 22 (1989), p. 377-433.
    • e série 22 (1989), p. 377-433.
  • 10
    • 57349191648 scopus 로고    scopus 로고
    • N. Burq, Mesures semi-classiques et mesures de défaut, Séminaire Bourbaki 39 (1996-1997), Exposé No. 826, p. 29.
    • N. Burq, Mesures semi-classiques et mesures de défaut, Séminaire Bourbaki 39 (1996-1997), Exposé No. 826, p. 29.
  • 11
    • 0035250971 scopus 로고    scopus 로고
    • The N-boson time dependent problem: An exact approach with stochastic wave functions
    • I. Carusotto, Y. Castin, and J. Dalibard, The N-boson time dependent problem: An exact approach with stochastic wave functions, Phys. Rev. A 63 (2001), 023606.
    • (2001) Phys. Rev. A , vol.63 , pp. 023606
    • Carusotto, I.1    Castin, Y.2    Dalibard, J.3
  • 12
    • 0000861319 scopus 로고    scopus 로고
    • Bose-Einstein condensates in atomic gases: Simple theoretical results
    • Coherent atomic matter waves, EDP Sciences and Springer-Verlag
    • Y. Castin, Bose-Einstein condensates in atomic gases: Simple theoretical results, in 'Coherent atomic matter waves', Lecture Notes of Les Houches Summer School, p. 1-136, EDP Sciences and Springer-Verlag (2001).
    • (2001) Lecture Notes of Les Houches Summer School , pp. 1-136
    • Castin, Y.1
  • 13
    • 0033238569 scopus 로고    scopus 로고
    • A proof of the Gutzwiller semiclassical trace formula using coherent states decomposition
    • M. Combescure, J. Ralston, D. Robert, A proof of the Gutzwiller semiclassical trace formula using coherent states decomposition, Comm. Math. Phys. 202 (1999), no. 2, 463-480.
    • (1999) Comm. Math. Phys , vol.202 , Issue.2 , pp. 463-480
    • Combescure, M.1    Ralston, J.2    Robert, D.3
  • 14
    • 33750631293 scopus 로고    scopus 로고
    • Une version mesurable du théorème de Stone-Weierstrass
    • Y. Coudène, Une version mesurable du théorème de Stone-Weierstrass, Gaz. Math. 91 (2002), 10-17.
    • (2002) Gaz. Math , vol.91 , pp. 10-17
    • Coudène, Y.1
  • 16
    • 33750551506 scopus 로고    scopus 로고
    • Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate
    • L. Erdös, B. Schlein, H. T. Yau, Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate, Comm. Pure Appl. Math. 59 (2006), no. 12, 1659-1741.
    • (2006) Comm. Pure Appl. Math , vol.59 , Issue.12 , pp. 1659-1741
    • Erdös, L.1    Schlein, B.2    Yau, H.T.3
  • 17
    • 33846807694 scopus 로고    scopus 로고
    • Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems
    • L. Erdös, B. Schlein, H. T. Yau, Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems, Invent. Math. 167 (2007), no. 3, 515-614.
    • (2007) Invent. Math , vol.167 , Issue.3 , pp. 515-614
    • Erdös, L.1    Schlein, B.2    Yau, H.T.3
  • 19
    • 37049009679 scopus 로고    scopus 로고
    • J. Fröhlich, A. Knowles, A. Pizzo, Atomism and quantization, J. Phys. A. Math. Theor. 40 (2007), 30333045.
    • J. Fröhlich, A. Knowles, A. Pizzo, Atomism and quantization, J. Phys. A. Math. Theor. 40 (2007), 30333045.
  • 20
    • 33947404010 scopus 로고    scopus 로고
    • Mean-field and classical limit of many-body Schrödinger dynamics for bosons
    • J. Fröhlich, S. Graffi, S. Schwarz, Mean-field and classical limit of many-body Schrödinger dynamics for bosons, Comm. Math. Phys. 271, no. 3 (2007), 681-697.
    • (2007) Comm. Math. Phys , vol.271 , Issue.3 , pp. 681-697
    • Fröhlich, J.1    Graffi, S.2    Schwarz, S.3
  • 21
    • 57349172123 scopus 로고    scopus 로고
    • Equations de champ moyen pour la dynamique quantique d'un grand nombre de particules
    • P. Gérard, Equations de champ moyen pour la dynamique quantique d'un grand nombre de particules, Séminaire Bourbaki No. 930 (2004).
    • (2004) Séminaire Bourbaki , Issue.930
    • Gérard, P.1
  • 22
    • 57349138934 scopus 로고
    • Séminaire sur les Équations aux Dérivées Partielles, Exp, 19 pp, École Polytech, Palaiseau, 1991
    • P. Gérard, Mesures semi-classiques et ondes de Bloch, Séminaire sur les Équations aux Dérivées Partielles, 1990-1991, Exp. No. XVI, 19 pp., École Polytech., Palaiseau, 1991.
    • (1990) Mesures semi-classiques et ondes de Bloch , Issue.XVI
    • Gérard, P.1
  • 24
    • 34250400047 scopus 로고
    • The classical field limit of scattering theory for nonrelativistic many-boson systems. I
    • J. Ginibre, G. Velo, The classical field limit of scattering theory for nonrelativistic many-boson systems. I., Comm. Math. Phys. 66, no. 1 (1979), 37-76.
    • (1979) Comm. Math. Phys , vol.66 , Issue.1 , pp. 37-76
    • Ginibre, J.1    Velo, G.2
  • 26
    • 0011563687 scopus 로고
    • Integration and nonlinear transformations in Hilbert space
    • L. Gross, Integration and nonlinear transformations in Hilbert space, Trans. Amer. Math. Soc. 94 (1960).
    • (1960) Trans. Amer. Math. Soc , vol.94
    • Gross, L.1
  • 28
    • 0007413567 scopus 로고
    • Around a stationary phase theorem in large dimension
    • B. Helffer, Around a stationary phase theorem in large dimension, J. Funct. Anal. 119 (1) (1994), 217252.
    • (1994) J. Funct. Anal , vol.119 , Issue.1 , pp. 217252
    • Helffer, B.1
  • 29
    • 33751565043 scopus 로고
    • Ergodicité et limite semi-classique
    • B. Helffer, A. Martinez, D. Robert, Ergodicité et limite semi-classique, Comm. Math. Phys. 109 (1987), no. 2, 313-326.
    • (1987) Comm. Math. Phys , vol.109 , Issue.2 , pp. 313-326
    • Helffer, B.1    Martinez, A.2    Robert, D.3
  • 31
    • 57349192889 scopus 로고    scopus 로고
    • B. Helffer, J. Sjöstrand, Semiclassical expansions of the thermodynamic limit for a Schrödinger equation. I. The one well case, Méthodes Semi-Classiques, 2, Astérique, 210, S.M.F., Paris, 1992.
    • B. Helffer, J. Sjöstrand, Semiclassical expansions of the thermodynamic limit for a Schrödinger equation. I. The one well case, Méthodes Semi-Classiques, Vol. 2, Astérique, Vol. 210, S.M.F., Paris, 1992.
  • 32
    • 33846791634 scopus 로고
    • The classical limit for quantum mechanical correlation functions
    • K. Hepp, The classical limit for quantum mechanical correlation functions, Comm. Math. Phys. 35 (1974), 265-277.
    • (1974) Comm. Math. Phys , vol.35 , pp. 265-277
    • Hepp, K.1
  • 35
    • 57349140813 scopus 로고
    • Une condition nécessaire et suffisante d'éllipticité pour une classe d'opérateurs différentiels en dimension infinie
    • B. Lascar, Une condition nécessaire et suffisante d'éllipticité pour une classe d'opérateurs différentiels en dimension infinie, Comm. Partial Differential Equations 2 (1977), no. 1, 31-67.
    • (1977) Comm. Partial Differential Equations , vol.2 , Issue.1 , pp. 31-67
    • Lascar, B.1
  • 36
    • 0001314058 scopus 로고
    • Sur les mesures de Wigner
    • P. L. Lions, T. Paul, Sur les mesures de Wigner, Rev. Mat. Iberoamericana 9 (1993), no. 3, 553-618.
    • (1993) Rev. Mat. Iberoamericana , vol.9 , Issue.3 , pp. 553-618
    • Lions, P.L.1    Paul, T.2
  • 38
    • 0003359771 scopus 로고
    • Quantum probability for probabilists
    • Springer-Verlag, Berlin
    • P. A. Meyer, Quantum probability for probabilists, Lecture Notes in Mathematics 1538, Springer-Verlag, Berlin, 1993.
    • (1993) Lecture Notes in Mathematics , vol.1538
    • Meyer, P.A.1
  • 39
    • 33748937848 scopus 로고    scopus 로고
    • Convergence of domain decomposition methods via semi-classical calculus
    • F. Nataf, F. Nier, Convergence of domain decomposition methods via semi-classical calculus, Comm. Partial Differential Equations 23 (1998), no. 5-6, 1007-1059.
    • (1998) Comm. Partial Differential Equations , vol.23 , Issue.5-6 , pp. 1007-1059
    • Nataf, F.1    Nier, F.2
  • 40
    • 21344438565 scopus 로고    scopus 로고
    • Classical limit of the harmonic oscillator Wigner functions in the Bargmann representation
    • N. Ripamonti, Classical limit of the harmonic oscillator Wigner functions in the Bargmann representation, J. Phys. A: Math. Gen. 29 (1996), 5137-5151.
    • (1996) J. Phys. A: Math. Gen , vol.29 , pp. 5137-5151
    • Ripamonti, N.1
  • 43
    • 0003845764 scopus 로고
    • 2 Euclidean (quantum) field theory
    • Princeton University Press, N.J
    • 2 Euclidean (quantum) field theory, Princeton Series in Physics. Princeton University Press, N.J., 1974.
    • (1974) Princeton Series in Physics
    • Simon, B.1
  • 45
    • 35949020007 scopus 로고
    • Kinetic equations from Hamiltonian dynamics
    • H. Spohn, Kinetic equations from Hamiltonian dynamics, Rev. Mod. Phys. 52, no. 3 (1980), 569-615.
    • (1980) Rev. Mod. Phys , vol.52 , Issue.3 , pp. 569-615
    • Spohn, H.1
  • 46
    • 84974050752 scopus 로고
    • H-measures, a new approach for studying homogenization Oscillations and Concentration Effects in Partial Differential Equations
    • L. Tartar, H-measures, a new approach for studying homogenization Oscillations and Concentration Effects in Partial Differential Equations, Proceedings of the Royal Society Edinburgh 115-A (1990), 193-230.
    • (1990) Proceedings of the Royal Society Edinburgh , vol.115-A , pp. 193-230
    • Tartar, L.1


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