EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 5 / No 4 (2010) Math. Model. Nat. Phenom., 5 4 (2010) 54-72 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
Page(s) 54 - 72
DOI https://doi.org/10.1051/mmnp/20105403
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 http://arxiv.org/abs/0904.4514. [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 http://arxiv.org/abs/0812.2740. [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 http://arxiv.org/abs/0906.3277. [Google Scholar]
  9. T. Chen, N. Pavlović. Higher order energy conservation, Gagliardo-Nirenberg-Sobolev inequalities, and global well-posedness for Gross-Pitaevskii hierarchies. Preprint http://arxiv.org/abs/0906.2984. [Google Scholar]
  10. T. Chen, N. Pavlović, N. Tzirakis. Energy conservation and blowup of solutions for focusing GP hierarchies. Preprint http://arXiv.org/abs/0905.2704. [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 http://arxiv.org/abs/0904.0158. [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.