Mean-field- and classical limit of many-body Schrödinger dynamics for bosons

Communications in Mathematical Physics

Volumn 271, Issue 3, 2007, Pages 681-697

  Fröhlich, Jürg ^a   Graffi, Sandro ^b   Schwarz, Simon ^a  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33947404010     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0207-5     Document Type: Article

References (16)

1. Bardos, C., Golse, F., Mauser, N.: Weak coupling limit of the n-particle Schrödinger equation. Methods Appl. Anal. 2, 275-293 (2000)
2. Bardos, C., Erdös, L., Golse, F., Mauser, N., Yau, H-T.: Derivation of the Schrödinger-Poisson equation from the quantum N-body problem. C.R. Acad. Sci. Paris 334, 515-520 (2002)
3. Bambusi, D., Graffi, S., Paul, T.: Normal forms estimates and quantization formulae. Commun. Math. Phys. 207, 173-195 (1999)
4. Braun, W., Hepp, K.: The Vlasov dynamics and its fluctuations in the l/N limit of interacting classical particles. Commun. Math. Phys. 56, 101-113 (1977)
5. Dobrushin R., L.: Vlasov equations. Sov. J. Funct. An. 13, 115-119 (1979)
6. Elgart, A., Erdös, L., Schlein, B., Yau, H.-T.: Nonlinear Hartree equation as the mean field limit of weakly coupled fermions. J. Math. Pures Appl. 83, 1241-1273 (2004)
7. Erdos, L., Yau, H.-T. : Derivation of the nonlinear Schrödinger equation from a many body coulomb system. Adv. Theor. Math. Phys. 5, 1169-2005 (2001)
8. Folland G.: Harmonic Analysis in Phase Space. Princeton, NJ: Princeton University Press, 1989
9. Graffi, S., Martinez, A., Pulvirenti, M.: Mean field approximation of quantum systems and classical limit. Math. Meth. Models in Appl. Sci. 13, 55-63 (2003)
10. Ginibre, J., Velo, G.: On a class of nonlinear Schrödinger equations with nonlocal interaction. Math. Z. 170, 109-136 (1980)
11. Hepp, K.: The classical limit for quantum mechanical correlation functions. Commun. Math. Phys 35, 265-267 (1974)
12. Lions P., L., Paul, T.: Sur les mesures de Wigner. Revista Matematica Ibero Americana 9, 553-618 (1993)
13. Narnhofer, H., Sewell, G.: Vlasov hydrodynamics of a quantum mechanical model. Commun. Math. Phys. 79, 9-24 (1981)
14. Robert D.: Autour de l'approximation semiclassique. Basel: Birkhäuser Verlag, 1987
15. Spohn, H.: Kinetic equations from hamiltonian dynamics: markovian limits. Rev. Mod. Phys. 53, 569-615 (1980)
16. Spohn, H.: On the Vlasov hierarchy. Math. Meth. Models in Appl. Sci. 3, 445-455 (1981)