Derivation of the nonlinear Schrödinger equation from a many body Coulomb system

2001/11/22 by Laszlo Erdos, Horng-Tzer Yau, Erdos, Laszlo +1 · 3 citations
Mathematics · Physics and Astronomy · #35Q55 #45F15 #81Q05 #81V70 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:35Q55 #msc:45F15 #msc:81Q05 #msc:81V70

paper · pdf · doi:10.48550/arxiv.math-ph/0111042

35 pages, latex

arxiv created 2002/05/22 · arxiv updated 2009/11/30

Abstract

We consider the time evolution of N bosonic particles interacting via a mean field Coulomb potential. Suppose the initial state is a product wavefunction. We show that at any finite time the correlation functions factorize in the limit N → ∞. Furthermore, the limiting one particle density matrix satisfies the nonlinear Hartree equation. The key ingredients are the uniqueness of the BBGKY hierarchy for the correlation functions and a new apriori estimate for the many-body Schrödinger equations.

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