Free Access
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
Page(s) 54 - 72
Published online 12 May 2010
  1. R. Adami, G. Golse, A. Teta. Rigorous derivation of the cubic NLS in dimension one. J. Stat. Phys., 127 (2007), No. 6, 1194–1220. [Google Scholar]
  2. M. Aizenman, E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason. Bose-Einstein Quantum Phase Transition in an Optical Lattice Model. Phys. Rev. A, 70 (2004), 023612. [CrossRef] [Google Scholar]
  3. I. Anapolitanos, I.M. Sigal. The Hartree-von Neumann limit of many body dynamics. Preprint [Google Scholar]
  4. V. Bach, T. Chen, J. Fröhlich andI.M. Sigal. Smooth Feshbach map and operator-theoretic renormalization group methods. J. Funct. Anal., 203 (2003), No. 1, 44-92. [CrossRef] [MathSciNet] [Google Scholar]
  5. T. Cazenave. Semilinear Schrödinger equations. Courant lecture notes, 10 (2003), Amer. Math. Soc.. [Google Scholar]
  6. T. Chen, N. Pavlović. The quintic NLS as the mean field limit of a Boson gas with three-body interactions. J. Functional Analysis, conditionally accepted. Preprint [Google Scholar]
  7. T. Chen, N. Pavlović. On the Cauchy problem for focusing and defocusing Gross-Pitaevskii hierarchies. Discr. Contin. Dyn. Syst., 27 (2010), No. 2, 715 - 739. [CrossRef] [Google Scholar]
  8. T. Chen, N. Pavlović. A short proof of local wellposedness for focusing and defocusing Gross-Pitaevskii hierarchies. Preprint [Google Scholar]
  9. T. Chen, N. Pavlović. Higher order energy conservation, Gagliardo-Nirenberg-Sobolev inequalities, and global well-posedness for Gross-Pitaevskii hierarchies. Preprint [Google Scholar]
  10. T. Chen, N. Pavlović, N. Tzirakis. Energy conservation and blowup of solutions for focusing GP hierarchies. Preprint [Google Scholar]
  11. A. Elgart, L. Erdös, B. Schlein, H.-T. Yau. Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons. Arch. Rat. Mech. Anal., 179 (2006), No. 2, 265–283. [Google Scholar]
  12. L. Erdös, B. Schlein, H.-T. Yau. Derivation of the Gross-Pitaevskii hierarchy for the dynamics of Bose-Einstein condensate. Comm. Pure Appl. Math., 59 (2006), No. 12, 1659–1741. [CrossRef] [MathSciNet] [Google Scholar]
  13. 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), 515–614. [CrossRef] [MathSciNet] [Google Scholar]
  14. L. Erdös, H.-T. Yau. Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. Adv. Theor. Math. Phys., 5 (2001), No. 6, 1169–1205. [MathSciNet] [Google Scholar]
  15. J. Fröhlich, S. Graffi, S. Schwarz. Mean-field- and classical limit of many-body Schrödinger dynamics for bosons. Comm. Math. Phys., 271 (2007), no. 3, 681–697. [CrossRef] [MathSciNet] [Google Scholar]
  16. J. Fröhlich, A. Knowles, A. Pizzo. Atomism and quantization. J. Phys. A, 40 (2007), No. 12, 3033–3045. [CrossRef] [MathSciNet] [Google Scholar]
  17. J. Fröhlich, A. Knowles, S. Schwarz. On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction. Preprint arXiv:0805.4299. [Google Scholar]
  18. M. Grillakis, M. Machedon, A. Margetis. Second-order corrections to mean field evolution for weakly interacting Bosons I. Preprint [Google Scholar]
  19. M. Grillakis, A. Margetis. A priori estimates for many-body Hamiltonian evolution of interacting boson system. J. Hyperbolic Differ. Equ., 5 (2008), No. 4, 857–883. [CrossRef] [MathSciNet] [Google Scholar]
  20. K. Hepp. The classical limit for quantum mechanical correlation functions. Comm. Math. Phys., 35 (1974), 265–277. [CrossRef] [MathSciNet] [Google Scholar]
  21. S. Klainerman, M. Machedon. On the uniqueness of solutions to the Gross-Pitaevskii hierarchy. Commun. Math. Phys., 279 (2008), No. 1, 169–185. [CrossRef] [Google Scholar]
  22. K. Kirkpatrick, B. Schlein, G. Staffilani. Derivation of the two dimensional nonlinear Schrödinger equation from many body quantum dynamics. Preprint arXiv:0808.0505. [Google Scholar]
  23. E.H. Lieb, R. Seiringer. Proof of Bose-Einstein condensation for dilute trapped gases. Phys. Rev. Lett., 88 (2002), 170409. [CrossRef] [PubMed] [Google Scholar]
  24. E.H. Lieb, R. Seiringer, J.P. Solovej, J. Yngvason. The mathematics of the Bose gas and its condensation. Birkhäuser (2005). [Google Scholar]
  25. E.H. Lieb, R. Seiringer, J. Yngvason. A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas. Commun. Math. Phys., 224 (2001) No. 1, 17–31. [CrossRef] [Google Scholar]
  26. I. Rodnianski, B. Schlein. Quantum fluctuations and rate of convergence towards mean field dynamics. Comm. Math. Phys., 29 (2009), No. 1, 31–611. [CrossRef] [Google Scholar]
  27. B. Schlein. Derivation of Effective Evolution Equations from Microscopic Quantum Dynamics. Lecture notes for the minicourse held at the 2008 CMI Summer School in Zurich. [Google Scholar]
  28. H. Spohn. Kinetic Equations from Hamiltonian Dynamics. Rev. Mod. Phys. 52 (1980), No. 3, 569–615. [CrossRef] [Google Scholar]
  29. T. Tao.Nonlinear dispersive equations. Local and global analysis. CBMS 106 (2006), AMS. [Google Scholar]

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