Quantum fluctuations and rate of convergence towards mean field dynamics

Igor Rodnianski, Benjamin Schlein

Research output: Contribution to journalArticlepeer-review

164 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)31-61
Number of pages31
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Aug 2009

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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