 05211 Riccardo Adami, Francois Golse, Alessandro Teta.
 Rigorous derivation of the cubic NLS in dimension one
(43K, LATeX 2e)
Jun 14, 05

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Abstract. We derive rigorously the onedimensional cubic nonlinear Schroedinger
equation from a manybody quantum dynamics. The interaction potential is
rescaled through a weakcoupling limit together with a shortrange one. We
start from a factorized initial state, and prove propagation of chaos with
the usual twostep procedure: in the former step, convergence of the
solution of the BBGKY hierarchy associated to the manybody quantum
system to a solution of the BBGKY hierarchy obtained from the cubic NLS
by factorization is proven; in the latter, we show the uniqueness for the
solution of the infinite BBGKY hierarchy.
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