05-211 Riccardo Adami, Francois Golse, Alessandro Teta.

Rigorous derivation of the cubic NLS in dimension one (43K, LATeX 2e) Jun 14, 05

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 05-211.tex