Rigorous derivation of the cubic NLS in dimension one

Journal of Statistical Physics

Volumn 127, Issue 6, 2007, Pages 1193-1220

  Adami, Riccardo ^a   Golse, François ^b   Teta, Alessandro ^c  

^a UNIVERSITY OF MILANO BICOCCA   (Italy)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

BBGKY hierarchy; Gross pitaevskii; Nonlinear schr dinger; Propagation of chaos; Quantum mechanics

Indexed keywords

EID: 34249868461     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9271-z     Document Type: Article

References (15)

1. R. Adami, C. Bardos, F. Golse and A. Teta, Towards a rigorous derivation of the cubic NLSE in dimension one. Asymptot. Anal. 40(2):93-108 (2004).
2. C. Bardos, L. Erdos, E Golse, N. Mauser and H.-T.Yau, Derivation of the Schrödinger-Poisson equation from the quantum N-body problem. C. R. Math. Acad Sci. Paris 334(6):515-520 (2002).
3. C. Bardos, E Golse and N. Mauser, Weak coupling limit of the N particles Schrödinger equation. Methods Appl. Anal. 7(2):275-293 (2000).
4. A. Elgart, L. Erdos, B. Schlein and H.-T. Yau, Gross-Pitaevskii equation as the mean field limit of weakly coupled Bosons. Math. Phys. preprint archive, mp-arc 04-333 (2004).
5. L. Erdos, private communication.
6. L. Erdos, B. Schlein and H.-T. Yau, Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate. Math. Phys. preprint archive, mp-arc 04-319 (2004).
7. L. Erdos, B. Schlein and H.-T. Yau, Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems, mp-arc 05-280.
8. L. Erdos, B. Schlein and H.-T. Yau, Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate, mp-arc 06-176.
9. L. Erdos and H.-T. Yau, Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. Adv. Theor. Math. Phys. 5(6):1169-1205 (2001).
10. J. Ginibre and G. Velo, The classical field limit of scattering theory for non relativistic many-boson systems. I and II. Comm. Math. Phys. 66:37-76 (1979),
11. and 68:45-68 (1979).
12. K. Hepp, The classical limit for quantum mechanical correlation functions. Comm. Math. Phys. 35:265-277 (1974).
13. E.H. Lieb, R. Seiringer and J. Yngvason, The Quantum-mechanical Many Body Problem: The Bose Gas. http://arxiv.org/abs/math-ph/?math-ph%2F0405004.
14. E. H. Lieb, R. Seiringer and J. Yngvason, One-dimensional behavior of dilute, trapped Bose gases. Comm. Math. Phys. 244(2):347-393 (2004).
15. H. Spohn, Kinetic equations from hamiltonian dynamics. Rev. Mod. Phys. 52(3):600-640 (1980).