Riccardo Adami, Francois Golse, Alessandro Teta.
Rigorous derivation of the cubic NLS in dimension one
(43K, LATeX 2e)
ABSTRACT. We derive rigorously the one-dimensional cubic nonlinear Schroedinger
equation from a many-body quantum dynamics. The interaction potential is
rescaled through a weak-coupling limit together with a short-range one. We
start from a factorized initial state, and prove propagation of chaos with
the usual two-step procedure: in the former step, convergence of the
solution of the BBGKY hierarchy associated to the many-body 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.