We derive rigorously the one-dimensional cubic nonlinear Schroedinger equation from a many-body quantum dynamics. The interaction potential is rescaled through a weakcoupling 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.
Rigorous derivation of the cubic NLS in dimension one / Riccardo, Adami; François, Golse; Teta, Alessandro. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 127:6(2007), pp. 1193-1220. [10.1007/s10955-006-9271-z]
Rigorous derivation of the cubic NLS in dimension one
TETA, Alessandro
2007
Abstract
We derive rigorously the one-dimensional cubic nonlinear Schroedinger equation from a many-body quantum dynamics. The interaction potential is rescaled through a weakcoupling 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
