Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Article type: Research Article
Authors: Adami, Riccardo; ; | Bardos, Claude; | Golse, François; | Teta, Alessandro;
Affiliations: Département de Mathématiques et Applications, École Normale Supérieure, Paris, France E‐mails: Riccardo.Adami, Francois.Golse@ens.fr | Université de Paris 7, Laboratoire Jacques‐Louis Lions, France E‐mail: bardos@math.jussieu.fr | Dipartimento di Matematica Pura ed Applicata, Università di L'Aquila, Italy E‐mail: teta@univaq.it
Note: [] Corresponding author. Current address: 45, rue d'Ulm, 75230 Paris cedex 05, France.
Note: [] One of us (R.A.) profited by a Marie Curie Fellowship, proposal n. MCFI‐2000‐01934, contract n. HPMF‐CT‐2000‐01102.
Note: [] Current address: 175, rue du Chevaleret, 750013 Paris, France.
Note: [] Current address: 45, rue d'Ulm, 75230 Paris cedex 05, France.
Note: [] Current address: Via Vetoio (Coppito 1), 67010 Coppito di L'Aquila (AQ), Italy.
Abstract: We consider a system of N particles in dimension one, interacting through a zero‐range repulsive potential whose strength is proportional to N−1. We construct the finite and the infinite Schrödinger hierarchies for the reduced density matrices of subsystems with n particles. We show that the solution of the finite hierarchy converges in a suitable sense to a solution of the infinite one. Besides, the infinite hierarchy is solved by a factorized state, built as a tensor product of many identical one‐particle wave functions which fulfil the cubic nonlinear Schrödinger equation. Therefore, choosing a factorized initial datum and assuming propagation of chaos, we provide a derivation for the cubic NLSE. The result, achieved with operator‐analysis techniques, can be considered as a first step towards a rigorous deduction of the Gross–Pitaevskii equation in dimension one. The problem of proving propagation of chaos is left untouched.
Journal: Asymptotic Analysis, vol. 40, no. 2, pp. 93-108, 2004
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
USA
Tel: +1 703 830 6300
Fax: +1 703 830 2300
sales@iospress.com
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
IOS Press
Nieuwe Hemweg 6B
1013 BG Amsterdam
The Netherlands
Tel: +31 20 688 3355
Fax: +31 20 687 0091
info@iospress.nl
For editorial issues, permissions, book requests, submissions and proceedings, contact the Amsterdam office info@iospress.nl
Inspirees International (China Office)
Ciyunsi Beili 207(CapitaLand), Bld 1, 7-901
100025, Beijing
China
Free service line: 400 661 8717
Fax: +86 10 8446 7947
china@iospress.cn
For editorial issues, like the status of your submitted paper or proposals, write to editorial@iospress.nl
如果您在出版方面需要帮助或有任何建, 件至: editorial@iospress.nl