Mean-field limit and semiclassical expansion of a quantum particle system

Annales Henri Poincare

Volumn 10, Issue 1, 2009, Pages 145-187

  Pezzotti, Federica ^a   Pulvirenti, Mario ^b  

^a UNIVERSITY OF L'AQUILA   (Italy)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 63949083006     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-009-0404-1     Document Type: Article

References (20)

1. C. Bardos, F. Golse, N. Mauser, Weak coupling limit of the N-particle Schrödinger equation, Methods Appl. Anal. 7 (2000).
2. C. Bardos, L. Erdos, F. Golse, N. Mauser, H.-T. Yau, Derivation of the Schrödinger-Poisson equation from the quantum N-body problem, C.R. Acad. Sci. Paris, Ser I. 334 (2002).
3. W. Braun, K. Hepp, The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles, Commun. Math. Phys. 56 (1977).
4. R. L. Dobrushin, Vlasov equations, Sov. J. Funct. Anal. 13 (1979).
5. L. Erdös, H.-T. Yau, Derivation of the nonlinear Schrödinger equation from a many body Coulomb system, Adv. Theor. Math. Phys. 5, No. 6 (2001).
6. L. Erdös, B. Schlein, Quantum Dynamics with Mean Field Interactions: A New Approach, Preprint arXiv 0804.3774v1.
7. J. Fröhlich, S. Graffi, S. Schwartz, Mean-field and classical limit of many-body Scrödinger dynamics for bosons, Commun. Math. Phys. 271 (2007), 681-697.
8. J. Fröhlich, A. Knowles, A. Pizzo, Atomism and quantization, J. Phys. A 40, No. 12 (2007).
9. J. Ginibre, G. Velo, The classical field limit of scattering theory for non-relativistic many-boson systems. I and II, Commun. Math. Phys. 66 and 68 (1979).
10. S. Graffi, A. Martinez, M. Pulvirenti, Mean-Field approximation of quantum systems and classical limit, Mathematical Models and Methods in Applied Sciences 13, No. 1 (2003), 59-73.
11. M. Hauray, P-E. Jabin, N-particles approximation of the Vlasov equations with singular potential, Arch. Rational Mech. Anal. 183 (2007).
12. K. Hepp, The classical limit for quantum mechanical correlation functions, Commun. Math. Phys. 35 (1974).
13. H. P. McKean, Propagation of chaos for a class of non-linear parabolic equations, Stochastic Differential Equations (Lecture Series in Differential Equations, Session 7, Catholic Univ.) (1967).
14. H. Narnhofer, G. Sewell, Vlasov hydrodynamics of a quantum mechanical model, Commun. Math. Phys. 79 (1981).
15. H. Neunzert, An introduction to the nonlinear Boltzmann-Vlasov equation, Lectures Notes Math. 1048 C. Cercignani (ed.), (1984).
16. M. Pulvirenti, Semiclassical expansion of Wigner functions, J. Math. Physics 47 (2006).
17. I. Rodnianski, B. Schlein, Quantum fluctuations and rate of convergence towards mean field dynamics, Preprint arXiv 0711.3087.
18. H. Spohn, Kinetic equations from Hamiltonian dynamics: Markovian limits, Review of Modern Physics, 53, No. 3 (1980).
19. H. Spohn, On the Vlasov hierarchy, Math. Methods Appl. Sci. 34 (1981).
20. E. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40 (1932).