Strengthened convergence of marginals  to the cubic nonlinear Schrödinger equation

Alessandro Michelangeli

doi:10.3934/krm.2010.3.457

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2010, Volume 3, Issue 3: 457-471. Doi: 10.3934/krm.2010.3.457

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Strengthened convergence of marginals to the cubic nonlinear Schrödinger equation

Alessandro Michelangeli^1,

1.
Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road CB3 0WB Cambridge

Received: February 2010

Revised: March 2010

Published: September 2010

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Abstract

We rewrite a recent derivation of the cubic non-linear Schrödinger equation by Adami, Golse, and Teta in the more natural form of the asymptotic factorisation of marginals at any fixed time and in the trace norm. This is the standard form in which the emergence of the non-linear effective dynamics of a large system of interacting bosons is proved in the literature.

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Mathematics Subject Classification: Primary: 70K99, 82C10, 82C22.

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