Quantum Fluctuations and Rate of Convergence Towards Mean Field Dynamics
- 255 Downloads
The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the rate of convergence of the microscopic quantum mechanical evolution towards the limiting Hartree dynamics. More precisely, we prove bounds on the difference between the one-particle density associated with the solution of the N-body Schrödinger equation and the orthogonal projection onto the solution of the Hartree equation.
Unable to display preview. Download preview PDF.
- 1.Adami, R., Golse, F., Teta, A.: Rigorous derivation of the cubic NLS in dimension one. Preprint: Univ. Texas Math. Physics Archive, http://www.ma.utexas.edu, No. 05-211, 2005
- 6.Erdős, L., Schlein, B., Yau, H.-T.: Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate. To appear in Ann. of Math. http://arxiv.org/abs/math-ph/0606017v3, 2006
- 8.Ginibre, J., Velo, G.: The classical field limit of scattering theory for non-relativistic many-boson systems. I and II. Commun. Math. Phys. 66, 37–76 (1979), and 68, 45–68 (1979)Google Scholar
- 12.Szegö, G.: Orthogonal Polynomials. Colloq. pub. AMS. V. 23, New York: Amer. Math. Soc., 1959Google Scholar