Archivio Istituzionale della RicercaWe derive rigorously the one-dimensional cubic nonlinear Schr¨odinger 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 / Adami, Riccardo; Golse, F.; Teta, A.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 127:(2007), pp. 1193-1220. [10.1007/s10955-006-9271-z]
Rigorous Derivation of the Cubic NLS in Dimension One
ADAMI, RICCARDO;
2007
Abstract
We derive rigorously the one-dimensional cubic nonlinear Schr¨odinger 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.
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https://hdl.handle.net/11583/2503854
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